It tells us that a toy has a mass of 3.0 kg, with a speed of 4.0 m/s.
We apply the following formula:
Ec = m * v²/2
We replace data and solve:
Ec = 3.0 kg* (4.0 m/s)²
Ec = 3.0 kg* 16 m²/s²/2
Ec = 48 kg * m²/s²/2
Ec = 24 kg * m²/s²
Ec = 24 N * m ========> Joules units
Ec = 24 J
The new cartia of the cart would be of 24 joules.
If a batter can apply the same amount of maximum force from their hands to each bat to swing it, why
would the speed of the bat swing decrease as the mass of the bat increases?
If a batter can apply the same amount of maximum force from their hands to each bat to swing it , the speed of the bat swing decrease as the mass of the bat increases because of greater moment of inertia .
Moment of inertia is directly proportional to the mass , hence if mass of the bat increased , moment of inertia will also increase and it will be more difficult to swing the bat .
hence , the speed of the bat swing decrease as the mass of the bat increases
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Scientists suspect that mars once had abundant liquid water on its surface. For this to have been true, early mars must have had __________ than mars today.
Scientists suspect that mars once had abundant liquid water on its surface. For this to have been true, early mars must have had a significantly greater atmospheric pressure and a far bigger greenhouse impact than mars today
What exactly is the greenhouse effect?The greenhouse effect describes how "greenhouse gases" trap heat at the Earth's surface. These heat-trapping gases act like a blanket wrapped around Earth, keeping it warmer than it would be without them. Carbon dioxide, methane, nitrous oxides, and water vapor are examples of greenhouse gases. Scientists have discovered that the warming effect of carbon dioxide aids in the stabilization of the Earth's atmosphere. The terrestrial greenhouse effect would collapse if carbon dioxide were removed. Without CO2, the Earth's surface would be 33°C (59°F) colder.
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the large blade of a helicopter is rotating in a horizontal circle. the length of the blade is 7.99 m, measured from its tip to the center of the circle. find the ratio of the centripetal acceleration at the end of the blade to that which exists at a point located 6.16 m from the center of the circle.
The ratio of the centripetal acceleration at the end of the blade to that which exists at a point located 6.16 m from the centre of the circle: 1.29
Centripetal acceleration is given by :
a = ω2R
where,
ω is the angular speed
R is the distance of the point from the centre
Let the point at the tip be A and that at distance 6.16 m from centre be B
Distance of point A from centre (RA) = 7.99 m
Distance of point B from centre (RB) = 6.16 m
Centripetal acceleration at A (aA) = ω2RA = 7.99ω2
Centripetal acceleration at B (aB) = ω2RB = 6.16ω2
The ratio (aA/aB) = 7.99/6.16 = 1.29
What is centripetal acceleration ?
centripetal acceleration is defined as the motion characteristic of an object moving along a circular path. Any object moving in a circle whose acceleration vector points towards the centre of that circle is called centripetal acceleration. You must have seen various examples of medium acceleration in your daily life. When you drive a car around a circle, your car experiences an average acceleration, and the average acceleration is also observed by a satellite orbiting the Earth. Middle means towards the centre.
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An experiment was performed to determine how the amount of coffee grounds could affect the taste of coffee. The same amount and type of water, the same perking time, and the same electrical sources were used. What is a constant?
A constant in the experiment performed to determine how the amount of coffee grounds could affect the taste of coffee is amount of water.
What is constant in an experiment?Experiment is a test under controlled conditions made to either demonstrate a known truth, examine the validity of a hypothesis, or determine the efficacy or likelihood of something previously untried.
An experiment is conducted using variables such as;
Independent variableDependent variableControlled variable or constantA controlled variable or constant is a factor that is kept constant in a series of experiments in which other factors are varied.
According to this question, in an experiment that was performed to determine how the amount of coffee grounds could affect the taste of coffee, the same amount and type of water, the same perking time, and the same electrical sources were used.
This suggests that the amount of water is a constant in this experiment.
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a ten-loop coil having an area of 0.23 m2 and a very large resistance is in a 0.047-t uniform magnetic field oriented so that the maximum flux goes through the coil. the coil is then rotated, so the flux goes to zero in 0.34 s. what is the magnitude of the emf induced in the coil during the 0.34 s?
The magnitude of electromotive force is 0.32 volts.
We need to know about the electromotive force of induction to solve this problem. The emf induction appears when there is any change in magnetic flux. The magnitude of emf can be determined by
ε = N dΦ / dt
where N is coil turns, ε is electromotive force, dΦ is change in magnetic flux and dt is time interval.
From the question above, the parameters given are
B = 0.047 T
dt = 0.34 s
N = 10
A = 0.23 m²
Find the change in magnetic flux
dΦ = (B . A)
dΦ = ( 0.047 . 0.23 )
dΦ = 0.01081 Tm²
By substituting the given parameters, we can calculate electromotive force
ε = N . dΦ / dt
ε = 10 . 0.01081 / 0.34
ε = 0.32 volt
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an electron moves from one point a to point b. while moving, the electron remains on an equipotential surface created by nearby charges. what can you say about the speed of the electron as it moved?
At initial speed must the quarter back through the ball for it to reach the reciver.
What is initial speed
The initial speed is the velocity at which motion start.
Sol-
The horizontal velocity is Vi*cos38.6and the vertical velocity is Vi*sin38.6
horizontal
28.4=Vi*cos38.6 time find time in terms of Vi.
Vertical
hf=hi+Vi*sin38.6*t -1/2 g t^2
now hf=hi=0
so
0=Vi*sin 38.6-1/2 g t and put the expression you got for t, then solve for Vi. You will encounter the need for one trig identity.
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Minerals and vitamins are called
Answer:
micronutrients.
Explanation:
L=0.7m
m=2kg
Calculate the frequency of the pendulum
According to the given data the frequency of the pendulum is 0.595 Hz.
What is frequency and Hz?Frequency is defined as the rate of changes in current direction per second. It is given in hertz (Hz), an internationally recognised unit of measurement. One cycle per second is equal to one hertz. Cycles per second are represented by the unit hertz (Hz). A cycle is a full cycle of an opposing current or voltage wave.
What makes frequency important?The time rate of change observed in cyclical and periodic phenomena, such as mechanical motion, audio signals (sound), radio waves, and light, is specified by the frequency, an essential parameter in science and engineering.
Briefing:Calculate the period of oscillations formula is
T = 2π√(L/g)
T = 2 * π * √(0.7/9.80665)
T= 1.678 s
Then the frequency as the reciprocal of the period
f = 1/T
f =1/1.678
f = 0.595 Hz.
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suppose your friend tells you that light from the nearest star, alpha centauri, requires a time of about 4.37 light-years to reach the earth. what is incorrect about this statement? explain your reasoning
The statement is incorrect about the light year .
What is a light year ?
A Light year is the distance that light travels in a vacuum in one year.
The fastest thing we know is light, which travels through empty space at 186,000 miles or 300,000 kilometers per second. To give you an idea of how fast it is, light can circle the Earth about seven times in one second. Astronomers use the speed of light to measure distance in space. A light year (ly) is the distance that light can travel in one year. In one year, light travels approximately 5,880,000,000,000 miles or 9,460,000,000,000 kilometers. So this distance is 1 light year. For example, our closest star is about 4.3 light years away. Our galaxy, the Milky Way, is about 150,000 light-years across, and the nearest large galaxy, the Andromeda Galaxy, is 2.3 million light-years away from her.
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if light of wavelength 257 nm is shined on a metal surface, electrons are ejected from the metal surface with a velocity 6.80 x 105 m/s. what is the wavelength of the ejected electrons?
The wavelength released during photoelectric effect is 353 nm.
We need to know about the photoelectric effect to solve this problem. The photoelectric effect is electron ejected from metal because of light source. The kinetic energy of the ejected electron is
K = (hc / λ) - (hc /λo)
where K is kinetic energy, h is Max Planck constant (6.6 x 10¯³⁴ Js), λ is the wavelength of light source and λo is the wavelength released from the metal.
From the question above, we know that
λ = 257 nm = 257 x 10¯⁹ m
c = 3 x 10⁸ m/s
v = 6.8 x 10⁵ m/s
me = 9.1 × 10¯³¹ kg
Find the wavelength released
K = hc . (1/λ - 1/λo)
1/2 . me .v² = 6.6 x 10¯³⁴ x 3 x 10⁸ . (1/257 x 10¯⁹ - 1/λo)
1/2 . 9.1 × 10¯³¹ . (6.8 x 10⁵)² = 6.6 x 10¯³⁴ x 3 x 10⁸ . (1/257 x 10¯⁹ - 1/λo)
2.10 x 10¯¹⁹ = 1.98 x 10¯²⁵ . (1/257 x 10¯⁹ - 1/λo)
2.10 x 10¯¹⁹ = (7.70 x 10¯¹⁹) - (1.98 x 10¯²⁵ / λo)
(1.98 x 10¯²⁵ / λo) = 5.60 x 10¯¹⁹
λo = 0.353 x 10¯⁶ m
λo = 353 nm
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The of earth’s orbit is among the planet’s unique characteristics. this characteristic allows water to exist in solid, liquid, and gas forms on earth. earth’s distance from the as well as the near- nature of its orbit, allow this phenomenon to take place.
It is distinguished from the other planets by the presence of liquid water on its surface, the presence of life, and active plate movement. It rotates on its axis once every 24 hours (a day) and orbits the Sun once every 365 days (a year). The Earth has a single moon.
What are the unique characteristics of Earth that allows the existence of life? It is the proper distance from the Sun, its magnetic field protects it from harmful solar radiation, an insulating atmosphere keeps it warm, and it contains the necessary chemical ingredients for life, including water and carbon.The Earth's orbit around the Sun is an ellipse, and the eccentricity measures how far the orbit deviates from a circle . The point on the orbit closest to the Sun is known as the perihelion, and the point farthest from the Sun is known as the aphelion.To learn more about : Earth's orbit
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what is the maximum speed (umax) that the missile could achieve in level flight? (hint: (1) when thrust is equal to the drag, there is no acceleration which means maxi speed. we assumed no drag, so it means when maxi speed is reached, the thrust is 0. (2) at this point, air reaches its maximum temperature, and no fuel injection is needed.) b) what would the velocity be of the gas exiting the nozzle (i.e., ue) at this maximum operating flight speed? c) sketch (qualitatively) the ramjet cycles for both cases (u
a) maximum speed (umax) that the missile could achieve in level flight = 2123 m/s
b) velocity of the gas exiting the nozzle (i.e., ue) at this maximum operating flight speed = 2120 m/s
The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar quantity. In essence, velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate.
Given data:
Pressure ratio = 45.5
TSFC = 5.27 * 10⁻⁵ kg/N
Cp = 1150 J/Kg
Wair = 25.5
Ta = 240K
Δhe = 4.4 KJ/kg
Tmax = 2200 K
(a) Maximum speed (Umax):
Ramjet's energy equation:
T₀₂ = Ta + (μ² / 2μ)
[tex]Umax = \sqrt{2Cp (Tmax - Ta})[/tex]
[tex]Umax = \sqrt{2* H50(2200 - 240)}\\ \\Umax = \sqrt{2 * 1150 * 1960}[/tex]
Therefore, Umax = 2123 m/s
(b) Velocity of exiting gas (Ue)
No fuel is provided, thus air expands back to its initial speed i.e., (Ue = U)
The specific thrust = [1 + f] Ue - U = 0
Therefore, Ue = 2120 m/s
(c) T-S diagram of Ramjet cycle:
The T-S schematics for Ramjet at U < Umax and U = Umax are based on the aforementioned two components ( 'a' and 'b')
Ramjets' maximum operating speed is significantly constrained by their maximum operating temperature.
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josh and taylor, standing face-to-face on frictionless ice, push off each other, causing each to slide backward. josh is much bigger than taylor. after the push, which of the two is moving faster?
After the push, Taylor will be moving faster because he has a smaller mass.
What is the force applied by each person?The force exerted by each person is determined by applying Newton's second law of motion.
F = ma
where;
m is the mass of the persona is the acceleration of the personThe force applied by each person depends on the mass and acceleration.
mass of Josh > mass of Taylor
Since Josh has a greater mass, he will be able impact more force on Taylor causing Taylor to move faster after the push.
Thus, the speed of each person after the push, depends on the force received by each person at the opposite end.
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the shape of an atomic orbital is associated with group of answer choices the spin quantum number (ms). the principal quantum number (n). the angular momentum quantum number (l). the magnetic quantum number (ml). the magnetic and spin quantum numbers, together.
The shape of an atomic orbital is associated with the principal quantum number (n).
Why do atoms have orbitals?
The wave character of the electrons (or electron pairs) in an atom is described by atomic orbitals, which are mathematical functions. They provide a method for calculating the likelihood that an electron will be located in a particular area surrounding the atom's nucleus. An atom can have any number of orbitals, according to the quantum atomic model.
Why do a wave's orbitals affect the shape of the wave?The function of the wave will therefore be determined by the distance from the nucleus and not by its direction. Any particle's orbital shrinks in size but maintains a spherical geometry as its center quantum number drops.
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What conditions must be met in order for work to be done?
Check all that apply.
A. The applied force must make the object move.
B. At least part of the applied force must be in the same direction as
the movement of the object.
c. The output force must be greater than the input force.
D. The work must be greater than the momentum. you
Answer: B) force must be in the same direction as movement
Explanation:
"That's just the tip of the iceberg" is a popular expression you may have heard. It means that what you can see is only a small part of the overall problem. As the diagram shows, most of an iceberg is actually out of sight, below the water level. Based on this diagram, what is the most likely density of the iceberg? (Assume a density of 1.03 g/mL for seawater.)
The possible density of the iceberg from the options that have been given in the question is 0.88 g/mL.
What is the iceberg?We know that the term density has to do with the ratio of the mass to the volume of an object. Now when we find that an object is denser than another, the denser object would tend to sink on the one that has a lesser density.
In accordance with the floatation principle which states that an object would displace only its own volume of the fluid. We can see that even if an object has an equal density as the other then it can float on the other liquid.
Here we have been shown the image of an iceberg which is close to what we have known as the "tip of the iceberg". We are now being asked to be able to obtain what should be the accurate density of the iceberg.
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Victor is using his Geiger-counter to record the amount of radiation that is leaking into the soil from a nearby nuclear disposal site. This radiation decreases by the square of the distance from the source. If he starts measurements 100 m from the disposal site how close will he need to stand if he hopes to measure soil with 4 times the radiation?
According to inverse square proportionality, measuring 4 times more radiation will require Victor to _____ his distance. Victor will need to stand _____ m from the disposal site.
If Victor starts measurements 100 m from the disposal site, he needs to stand 50 m from the source if he hopes to measure soil with 4 times the radiation.
I = 1 / r²
I = Intensity
r = Distance
At a distance of 100 m from the source,
I = 1 / 100²
I = 1 / 10000
I = [tex]10^{-4}[/tex] J / m² s
Four times this radiation will have an intensity of,
I = 4 * [tex]10^{-4}[/tex] J / m² s
4 * [tex]10^{-4}[/tex] = 1 / d²
d² = 1 / 4 * [tex]10^{-4}[/tex]
d² = 0.25 * [tex]10^{4}[/tex]
d = √ 25 * 10²
d = 5 * 10
d = 50 m
Therefore, he needs to stand 50 m from the source
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during a tennis match, a player serves the ball at 23.6 m/s, with the center of the ball leaving the racquet horizontally 2.37 m above the court surface. the net is 12m away and 0.90 m high. when the ball reaches the net, a) does the ball clear it? show your solution. b) what is the distance between the center of the ball and the top of the net?
a) Yes the ball clear it. Through, equation of motion is 1.104 m > 0.9 m
b) The distance between the center of the ball and the top of the net is 0.204 m
a) As we know the equation of motion,
y = 1/2(at^2)
y= 1/2 (9.81)(0.508)^2
y = 1.266 m
height = Y net - y
h = 2.37m - 1.266m
h = 1.104m
b)
height in y direction - net height
= 1.104m - 0.9m
= 0.204m
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in a computational model of the energy loss of a house, if the energy flux increases and the total area insulated increases, what happens to the energy loss of the house?
The energy loss can increase or decrease.
In modern houses and systems, insulation is created to maintain heat and reduce losses.
P = ( AΔT ) / R
P is the heat flow, A is the insulated area, T is the temperature difference, and R represents the correlation between the insulation's thermal conductivity and thickness.
In this instance, they suggest that both the flow and the isolated area are growing. We have numerous options.
In this instance, the flow grows faster than the isolated area, increasing heat loss.
The quantity of insulation needed to increase (R) will cause the heat flow to grow by the same amount as the isolated area while keeping losses constant
Losses will reduce if the rate of heat transfer increases more slowly than the area that is insulated.
The two rises in this instance suggest that the heat requests may increase or decrease.
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If a tenth planet were to be discovered with a sidereal period of 125 years, what would be the radius or the orbit (distance from the Sun)? In your answer you need to have the number in the first blank and the correct abbreviated units in the second blank.
From the computation and the use of the Kepler's law, the period of the orbit is period of the orbit is 25 AU.
What is Kepler's law?The term Kepler's law has to do with the relationship between the relationship between the period of the satellite and the radius of the orbit in which the satellite is found.
According to the Kepler's law, we know that the square of the period of the satellite is directly proportional to the cube of the radius of the orbit. Having said this, we need to find the radius of the orbit and we have been told from the question as we have it above that the period of the satellite that is under consideration is 125 years.
Now;
T^2 = r^3
Given that;
T = period
r = radius of the orbit
Then;
r = T^2/3
r = (125)^2/3
r = 25 Au
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a car travelling at a speed of 45km/h takes 20 minutes to reach its destination.what distance has the car travelled
First, we need to do a type conversion. Because the types of the two given quantities are different. One is in minutes. The other is in hours. A vehicle that travels [tex]45[/tex] kilometers in an hour travels how many meters in a second?
[tex]45km/h=\frac{45km}{1hour} =\frac{45km.1000}{1hour.3600} =12.5m/s[/tex]A vehicle that travels [tex]12.5[/tex] meters in a second travels how many meters in [tex]20[/tex] minutes?
[tex]1200.(12.5)=15000m=15km[/tex]help plssss
Your car is traveling at an initial speed of Vo. At t = 0, you start increasing your speed at a constant acceleration. After 20s, the speed of the car is 54 km/ h, after 60 s — 108 km/ h.
a) What was your acceleration?
b) What was your initial speed?
c) What was the speed after 40s?
Given Data:
The applied acceleration is constant.
speed of the car after time,t1 = 20s, is V1= 54 km/h = 15 m/s
speed of the car after time,t2 = 60s, is V2= 108 km/h = 30m/s
we use the formula, V = Vo + a x t
where, Vo is the initial speed, a is the acceleration(constant),
t is the time taken by the object.
a) Acceleration = rate of change of speed with time = V2 - V1 / t2 - t1
a = 30-15/60-20
a = 15/40 = 0.375 m/[tex]{s^{2} }[/tex]
b) Initial speed, Vo = V1 - a x t1
= 15 - 0.375 x 20
= 7.5 m/s
c) Speed after 40 s, V = Vo + a x t, t = 40s
= 7.5 + 0.375 x 40
= 22.5 m/s
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a navy blue car and a mint green cars drive on two different lanes of the same same very curved road. the radius of curvature of the path of the navy blue car, which has a mass of 1616 kg, is approximately 4/5 of that of the mint green car, which instead has a mass of 1818 kg. assume that neither car skids on the road. how do the static friction forces on the two cars compare, if the drivers are on the same street, both going at the local speed limit?
The friction force ratio between navy blue car and mint green car due to the centripetal force is 10/9.
We need to know about centripetal force to solve this problem. When an object moves in a circular motion, the object is experiencing centripetal force. The magnitude of centripetal force is
Fc = m . v²/R
where Fc is the centripetal force, m is mass, v is velocity and R is the radius.
The friction force is proportional to the centripetal force
From the question, we know that
mblue = 1616 kg
mgreen = 1818 kg
Rblue = 4/5 Rgreen
vblue = vgreen
Find the centripetal force ratio
Fcblue / Fcgreen = (mblue . vblue² / Rblue) / (mgreen . vgreen² / Rgreen)
Fcblue / Fcgreen = (1616 / 4/5 Rgreen ) / (1818 / Rgreen)
Fcblue / Fcgreen = 10 / 9
Hence, the tension in the cord is 32 newton.
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Cocoa is made from _______. a. cacao beans b. cacao leaves c. the meat of the cacao fruit d. milk, butter, sugar and cacao fruit please select the best answer from the choices provided a b c d
The correct option is (a) Cocoa beans are used to make cocoa.
Cocoa bean shapes during manufacture The dried and fully fermented seed of Theobroma cacao, usually known as the cocoa bean or simply cocoa, is where cocoa solids and cocoa butter are extracted.
The dried, fully fermented cacao grain known as Theobroma is what is commonly referred to as a cacao bean or a cocoa bean. Solids, a mixture of nonfat substances, and cocoa butter, or lard, can be extracted from Theobroma cacao. The chocolate and meals from Mesoamerica were made from these cacao beans. As a result, cacao beans are used to create chocolate.
Hence, cocoa is made from cocoa beans.
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a cave rescue team lifts an injured spelunker directly upward and out of a sinkhole by means of a motor-driven cable. the lift is performed in three stages, each requiring a vertical distance of 10.0 m. (1) first, the initially stationary spelunker is accelerated to a speed of 5.30 m/s. (2) then he is then lifted at the constant speed of 5.30 m/s. (3) finally he is decelerated to zero speed. how much work is done on the 73.0 kg rescuee by the force lifting him during each stage?
Mass m = 73kg
Vertical height in each stage h = 10 m
A). Initial speed u = 0
Final speed v = 4.3m / s
Work done W= mgh + ( 1/ 2) m[v 2 - u 2 ]
= 7063.2 +665.64
= 7728.84 J
B).Work done W = mgh
= 7063.2J
C).Work done W = mgh + ( 1/ 2) m [ V 2 - v 2 ]
Where V = final speed
= 0
v =4.3m / s
Substitute the values we get W =7063.2 - 665.64
= 6397.56 J
To slow down a vehicle The vehicle slows down when it sees a police car. Thesaurus synonyms, antonyms, and examples. slow down. Slowing down The car slowed down and stopped next to her. A motionless object has zero velocity. If an object has zero acceleration its velocity must be constant.
Whenever an object's acceleration is in the same direction as its velocity, the car is accelerating and is said to be accelerating. If the acceleration is simultaneously opposed to the speed, the car is said to be slower and slower. Delay slows down: An unexpected slowdown in your car could mean you're running out of gas.
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Show how you got the answer, please
Question:
A wave with a frequency of 14 Hz has a wavelength of 3 meters. At what speed with this wave travel?
Answer:
42m/s
Explanation:
v= λf
Frequency of wave: f= 14Hz
the wavelength of the wave: λ=3m
speed of wave: s=?
speed = frequency * wavelength
s = 14 * 3 = 42 m/s.
what is the maximum speed with which a 1200- kgkg car can round a turn of radius 95.0 mm on a flat road if the coefficient of static friction between tires and road is 0.60?
The maximum speed will be 0.74m/s
What is friction force?Friction, the force that resists a solid object from sliding or rolling over another. Frictional forces, such as the traction required to walk without slipping, can be beneficial, but they also present significant resistance to motion. About 20% of a car's engine power is expended to overcome the frictional forces of moving parts.
The speed that corresponds to the maximum centripetal force (Fₓ) that could be provided by the friction is given as:
f = Fₓ
f = μN is the friction force. where, μ is the coefficient of static friction and this is the maximum force the friction can provide.
Fₓ = mv²/r
N = mg (flat road)
Thus:
μ mg = mv²/r
So, according to the given question:
μ = 0.60
m = 1200kg
r = 95.0 mm or 95×10⁻³m
μ mg = mv²/r
0.60 × 9.8 = v²/ 95×10⁻³
v² = 558.6 ×10⁻³
v = 0.74m/s
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cepheid stars are useful to astronomers as indicators of group of answer choices white-dwarf star behavior. the mechanics of eclipsing variable stars. distance, particularly to stars in our galaxy and to nearby galaxies. stars with very high speed motion.
Option b cepheid stars are useful to astronomers as indicators of distance, particularly to stars in our Galaxy and to nearby galaxies.
An astronomer is a scientist who focuses on the stars, planets, galaxies and other extraterrestrial natural phenomena. The study of astronomy includes everything in the cosmos that is outside of our solar system. This includes celestial bodies that we can see with our unaided eyes, such as the Sun, Moon, planets, and stars. Additionally, it contains celestial bodies like distant galaxies and minute particles that we can only see with telescopes or other tools. On a more urgent level, astronomy aids in our research into how to extend the survival of our species. Studying the Sun's impact on Earth's climate and how it will effect weather, water levels, etc., for instance, is crucial. The broad discipline of natural science known as astronomy is concerned with celestial objects, such as those in the solar system, galaxies, and extragalactic objects. The majority of the fieldwork participants are students who specialize in this broad discipline.
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A golfer takes three strokes to putt a golf ball into a hole. On the first stroke, the ball moves 5.1 m due east. On the second, it moves 1.8 m at an angle 20° north of east. On the third, it moves 0.50 m due north. If the golfer had instead hit the ball directly into the hole on the first stroke, what would have been the magnitude (in m) and direction of the ball's displacement? Give the direction as a positive angle measured counterclockwise from due east.
The three strokes to put the golf ball into a hole is given. we have to find the overall displacement of the golf ball and its direction measured counterclockwise due east. So, we take due east as 0°, north as 90°, and so on.
For 1st stroke, the ball moves 5.1m due east means 5.1m at 0°.
The displacement along x- direction for 1st stroke = 5.1m × cos 0° = 5.1m, and y-displacement = 5.1m × sin 0° = 0m.
For 2nd stroke, the ball moves 1.8m at an angle 20° north of east.
Its x-displacement = 1.8m × cos (20°) = 1.691m, and y-displacement = 1.8m × sin (20°) = 0.6156m.
For third stroke, the ball moves 0.50m due north, means 0.50m by 90°.
Its x-displacement = 0.5m × cos (90°) = 0m, and y-displacement = 0.5m × sin(90°) = 0.5m.
The overall x- and y- displacements of the ball are:
x = 5.1 + 1.691 + 0 m = 6.791 m, and
y = 0 + 0.6156 + 0.5 m = 1.1156 m, respectively.
And its direction is θ = y/x = 1.1156 ÷ 6.791 = 0.164° due east.
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HELP!
Emily is riding her skateboard down the sidewalk at 2 m/s when she suddenly hits a rock, causing the skateboard to stop. According to Newton's first law of motion, what happens to Emily?
a
Emily accelerates forward.
b
Emily moves forward at 2 m/s.
c
Emily moves forward at less than 2 m/s.
d
Emily stops with her skateboard.
Answer: (b)
Explanation:
According to the law of conservation of momentum.
B. Emily moves forward at 2 m/s.