Jack and Jill takes 14 minutes to walk 340 m [West], then 129 m [South]. Calculate
a. their total displacement
b. their average speed
c. their average velocity

The magnitude of the average force exerted by the seat belt on the dummy is 224N .

The average force is the force produced by an object moving over a specific period of time at a given rate of speed, or velocity. This velocity is not instantaneous or precisely measured, as the word "average" indicates.

mass of the dummy (m) = 80kg

velocity of the dummy (v) = 28 m/s

time (t) = 10 seconds

Average force exerted (F)

To calculate the average force;

According to the formula;

F = (m × v) ÷ t

Where;

F represents the force exerted

m represents the mass of the dummy

v represents the velocity

t represents the time

F = m * v/t

F = 80 *28/10

F = 224

F = 224 N

The force exerted by the seat belt on the dummy is 224N .

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Satellite B's radius will be less than Satellite A's radius.

m = Satellite Mass

v = Satellite Velocity

r = Orbital radius of the satellite

Relating the gravitational and centripetal forces

mv^2/ r= GmM/r^2

v^2/r=GM/r^2

v^2=GM/r

v = sqrtGM/r

As can be shown, the mass of the satellite has no bearing on the relationship between velocity and radius.

This implies that the radius must shrink for v to increase

Here, vb>va

Therefore, satellite b's radius will be smaller than satellite a's radius.

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The mass of the mouse, m₁=0.042 kg

The mass of the 1st cart, m₂=0.35 kg

The mass of the second cart, m₃=0.25 kg

The speed of the 1st car after the jump, u₁=0.88 m/s

From the law of conservation of momentum, the momentum of a system should always remain the same.

Before the mouse jumps from one cart to another, all the objects were at rest. Therefore the total momentum of the system was zero.

Thus after the mouse jumps, the total momentum of the system should be equal to zero.

Thus the momentum of the second cart and the mouse will be equal in magnitude to the momentum of the first cart but it will be in the opposite direction.

Thus,

On substituting the known values,

Thus the speed of the mouse and the second cart after the mouse jumps is 1.05 m/s

The combination of the graphs that shows a free fall are A and C.

We know that motion has to do with the change of position with time. When an object is falling freely, the velocity of the object would remain constant because the velocity or the speed does not change.

Recall that when we throw objects down from a height, the objects would fall at the same rate irrespective of the masses of the objects. This can be understood to mean that the acceleration that acts on the objects is the same and does not change.

However, the distance that is covered by the object does change with tome and this can be seen from the graph as we have in the question. We can now see that the graph that has a flat speed time graph and a straight distance time graph can describe on object that is undergoing free fall.

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The energy of the photon of light as we can see here is 2.9 * 10-19 J.

We know that light has to do with any of the components of the electromagnetic spectrum. These are the kinds of radiation that are able to pass through vacuum because they do not need a medium for the propagation of the wave. We are now asked to obtain the energy of the photon based in the wavelength that we have been supplied in the question here.

We have that the wavelength of the photon from what we can see in the question have been given as 670 nm. Then;

E = hc/λ

E = energy of the light

h = Plank's constant

c = speed of light

λ = wavelength of the light

It then follows that;

E = 6.6 * 10^-34 * 3 * 10^8/670 * 10^-9

E = 2.9 * 10-19 J

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Answer:

Pascal (Pa)

Explanation:

the si for pressure is the pascal pa equal to one newton per sqaure meter (N/m^2, or kgxm-^1xs-^2)

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The mass of the car that was stuck is  1657 Kg.

We know that we have to use the laws of the conservation of the linear momentum here. It is known that the momentum before collision must be equal to the total momentum that we have after collision.

In this case, we have;

m1u1 + m2u2 = m1v1 + m2v2

m1  = mass of the truck

m2 = mass of the car

u1 and v1 = the initial and final velocities of the truck

u2 and v2 = initial and final velocities of the car

Again we are told that the two continue to move together hence v1 + v2 = v

m1u1 + m2u2 = (m1 + m2) v

(2900 * 11.0) + 0 = (2900  + m2) 7

31900 = 20300 + 7m2

31900 - 20300 = 7m2

m2 = 31900 - 20300 /7

m2 = 1657 Kg

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The acceleration of the baseball is 500 m/s².

A force is an influence that has the power to alter an object's motion. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull.

The mass of the baseball, m = 0.2 kg

The force acting on the baseball is 100 N.

By Newton's second law of motion,

F = ma

Substituting the values in the above equation,

100 N = 0.2 kg × a

a = 100 / 0.2

a = 500 m/s²

The total mass when the baseball and baseball bat are in contact is:

m = 0.2 + 0.94 = 1.14 kg

Then the acceleration will be:

F = ma

100 = 1.14 × a

a = 87.7 m/s²

The acceleration of the ball after the contact is 500 m/s².

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The importance of the pressure t exerted via the string connecting the bins evaluate to the value f is T< f.

A force is a power that can trade the movement of an object. A force can encourage an item with mass to exchange its tempo, i.e., to boost up. stress can also be described intuitively as a push or a pull. A strain has both importance and path, making it a vector quantity.

considering both masses together

The acceleration of the system = a

a = f/m+m = f/2m

Now, considering one mass towards left m

T = ma

T = (f/2m)

m = f/2

T = f/2

T<f

Therefore, T must have a magnitude less than f.

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The distance covered by the object is given as,

Plug in the known values,

Thus, the distance covered by the object is 81 m.

The main difference between Kinetic energy and Potential energy is that kinetic energy refers to movement while potential energy refers to storage.

Kinetic energy is a type of energy in motion or energy in movement such as a turbine (mechanical energy), while Potential energy refers to the energy that is stored to be used when required (e.g. chemical bonds of foods).

Therefore, with this data, we can see that  Kinetic energy is used as movement, while Potential energy is stored to be used in the future.

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Given,

The mass of the barbell, m=70 kg

The height to which Slim Jim lifts the barbell, h=1.4 m

a)

When the barbell was on the ground, it will have zero kinetic energy as it has no velocity. And if assume the height of ground as zero meters, then its potential energy is also zero.

Thus when the barbell was on the ground, its energy was zero joules.

b)

The energy of the barbell when it is at a height of h is given by,

Where g is the acceleration due to gravity.

On substituting the known values,

Thus the energy that the barbell has after being lifted 1.4 m is 960.4 J

This energy is the energy stored in the barbell due to its position. Thus the energy stored in the barbell is the potential energy.

Slim Jim has to do some work to lift the barbell to the given height. This work done will be stored in the barbell in the form of potential energy. That is, the energy of the barbell is supplied to it from Slim Jim through the work.

c)

All the work done by Jim will be stored in the barbell in the form of potential energy. Thus, the work done by Jim is equal to the potential energy of the barbel.

Therefore, the work done by Jim is 960.4 J

d)

Given,

The time interval, t=1.5 s

The power is given by,

Where W is the work done by Jim.

On substituting the known values,

Thus the power used by Jim is 640.27 W

From the Law of conservation of energy, we know that the sum of the kinetic and potential energy of the rocket is the same at the surface of the Earth and at the maximum altitude. Nevertheless, the kinetic energy of the rocket when it is at the maximum altitude is 0:

The kinetic energy is given by:

On the other hand, the gravitational potential energy for big changes in altitude (comparable to the radius of the Earth) is given by the expression:

Where M is the mass of the Earth, m is the mass of the rocket, r is the distance from the center of the Earth to the rocket and G is the gravitational constant:

At the beggining of the movement, the value of r corresponds to the radius of the Earth:

At the end of the movement, the value of r corresponds to the radius of the Earth plus the maximum altitude h:

Substitute the expressions for U_1, K_1 and U_2 and simplify the equation by eliminating the factor m:

Isolate the term GM/(R_E+h):

Divide both sides by the factor GM:

Take the reciprocal to both sides of the equation:

Isolate h:

Substitute the values of each variable: R_E=6.37x10^6m, M=5.98x10^24kg, G=6.67x10^-11 N*m^2/kg^2, and v=9.0x10^-3 m/s:

Therefore, the maximum altitude reached by a rocket with an initial speed of 9.0x10^3m is:

Answer: The wall and base

Explanation:

The Angular velocity is 54.55 rad/s

What is angular velocity?
The rate at which an angle between two bodies changes is known as angular velocity. Something changes when an object rotates or revolves around an axis. This displacement is depicted in the image by the angle formed by a line on just one body and a line on the other. Technical terms like degrees, 360-degree revolutions, as well as revolutions per minute have been frequently used to describe angles or angular displacements (rpm). Angles and angular velocities are typically expressed in radians as well as radians per second, respectively, in mathematics and physics.

These conversion factors link these measurements together:
A radian equals 1/180 (or 0.0175) of a degree, and a radian per second = 1/30 (or 0.105) of a radian.
Angular velocity W= U/r
Given V= 30m/s ; r=0.55mW=3/0.55 = 54.55 rad/s

Hence the answer is 54.55 rad/s

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Sphere, cylinder, hoop is the correct prediction. Moment of inertia is defined as the quantity represented by a body that resists an angular acceleration that is the sum of the product of each particle's mass times the square of its distance from the axis of rotation.

Ball moment of inertia Is = 2/5 M r²

Cylinder Ic = ½ M r²

Tire Ih = M r²

Substitute each to calculate time

Ball

ts = (d / √2gy) √ ( 1 + 2/5 Mr² / mr²)

ts = (d / √ 2gy) √ (1 +2/5) = (d / √ 2gy) √(1.4)

ts = (d / √ 2gy) 1.1

Cylinder

tc = (d / √2gy) √ (1 + 1/2 Mr² / Mr²)

tc = (d / √2gy) √ (1 + ½) = (d / √ 2gy) √ 1.5

tc = (d / √ 2gy ) 1.2

tires

th = (d / √2gy) √ (1 + mr² / mr²)

th = (d / √2gy) √(1 + 1) = (d / √ 2gy ) √ 2

th = ( d / √ 2gy) 1.41

The result is that the bullet hits the fastest and the body with the most tires. So the correct answer is

ts < . tc < th

ball, cylinder tire

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The amount of heat released outside is 3.5 kJ and the coefficient of performance is 2.

The efficiency of the a machine or any device is the measure of effectiveness of the device. Efficiency describes how a machine converts input energy to output energy without wasting much of the input energy.

Mathematically, efficiency of a machine is given as;

E = output energy / input energy  x 100%

The coefficient of performance  (COP) of a heat pump, refrigerator or air conditioning system is a ratio of useful heating or cooling provided to work required.

The energy released outside = 3.5 kJ

COP = 3.5 kJ / 1.75 kJ

COP = 2

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2.20 m/s^2  is the acceleration of the elevator.

Option c is correct answered .

If you stand on a scale in an elevator accelerating upward, you feel heavier because the elevator's floor presses harder on your feet, and the scale will show a higher reading than when the elevator is at rest. On the other hand, when the elevator accelerates downward, you feel lighter.

support force F = mass x acceleration + weight

For a mass m= kg, the elevator must support its weight = mg = Newtons to hold it up at rest. If the acceleration is a= m/s² then a net force= Newtons is required to accelerate the mass.

Fnet = m a

Fn + (-Fg) = m a

a = 1020 - (85)(9.8) /85

a = 2.20  m/s^2

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Answer:

a) Uniform rectilinear motion

b) 600 m

c) 20 m/s

Explanation:

a) average velocity is described as the change of position divided by the time of travel, so v= ∆x/∆t. This is a linear function (y = mx+ q) which is the same structure of the equation needed to calculate average velocity (x2= x1 + vt). If you do the ratio between a distance and the corresponding time you'll see that the average velocity is the same, which is typical of this kind of motion.

b) At the the time of 30 seconds the corresponding distance on the y axis is 600 m.

c) Again, v=∆x/∆t and we can rewrite is as v=x2-x1/t. If you take the same data we've used before you can write v= 600m-0/ 30s= 20 m/s. The average velocity is 20 m/s.

The freight train has a momentum of mv = (4.5 × 105 kg)(1.4 m/s) = 6.3 ×105 kg-m/s.

An automobile with a mass of 1800 kg would need to go at a speed of 6.3  × 105 kg-m/s ÷ 1800 kg = 350 m/s in order to have a momentum of the same magnitude. (Roughly 800 mph)

A moving body's amount of motion is referred to as momentum. It has units of kg m/s and is theoretically represented as p = m * v.

The momentum equation connects the total force exerted on a fluid element to its acceleration or rate of change of momentum and is a formulation of Newton's Second Law. You're certainly familiar with the formula F = ma, which links applied force and acceleration in solid mechanics analysis.

Momentum is the result of a particle's mass and velocity. Being a vector quantity, momentum possesses both magnitude and direction. According to Isaac Newton's second equation of motion, the force applied on a particle is equal to the time rate of change of momentum.

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The coefficient of static friction between the ramp of 75 cm horizontal length and a vertical length of 19 cm and object with a mass of 128 g is 0.25

Since the ramp forms a right angled triangle,

tan θ = Opposite side / Adjacent side

Opposite side = Vertical length of ramp = 19 cm

Adjacent side = Horizontal length of ramp = 75 cm

tan θ = 19 / 75

θ = [tex]tan^{-1}[/tex] ( 0.25 )

θ = 14°

m = 128 g = 0.128 kg

g = 9.8 m / s²

W = m g

W = 0.128 * 9.8

W = 1.25 N

Since the object is in static condition,

∑ [tex]F_{y}[/tex] = 0

N - [tex]W_{y}[/tex] = 0

N - W cos θ = 0

N = 1.25 * cos 14°

N = 1.25 * 0.97

N = 1.21 N

F[tex]_{s}[/tex] = μ[tex]_{s}[/tex] N

F[tex]_{s}[/tex] = Static frictional force

μ[tex]_{s}[/tex] = Co-efficient of static friction

N = Normal force

Since the object is in static condition,

∑ [tex]F_{x}[/tex] = 0

F[tex]_{s}[/tex] - [tex]W_{x}[/tex] = 0

F[tex]_{s}[/tex] = W sin θ

F[tex]_{s}[/tex] = 1.25 * sin 14°

F[tex]_{s}[/tex] = 1.25 * 0.24

F[tex]_{s}[/tex] = 0.3 N

μ[tex]_{s}[/tex] = F[tex]_{s}[/tex] / N

μ[tex]_{s}[/tex] = 0.3 / 1.21

μ[tex]_{s}[/tex] = 0.25

Therefore, the coefficient of static friction between the ramp and object is 0.25

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When a mass attached to a spring, it will make the spring to produce a harmonic motion with frequency 1.4 Hz. Then the mass is 77.48 gram.

The frequency of a harmonic motion caused by a displaced spring is:

f = 1/2π . √(k/m)

Where:

k = spring constant

m = mass

Parameters given from the problem:

f = 1.4 Hz

k = 6 N/m

Plug those parameters into the formula:

1.4 = 1/2π . √(6/m)

√(6/m) = 8.8

m = 0.07748 kg = 77.48 gram

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The element that has 4 electrons, 3 protons and 6 neutrons is lithium ion.

An element is one of the simplest chemical substances that cannot be decomposed in a chemical reaction or by any chemical means and made up of atoms all having the same number of protons.

The atom of an element is made up of three subatomic particles namely;

In a neutral element, the number of protons and electrons are the same i.e. equal. According to this question, an element has 4 electrons, 3 protons and 6 neutrons.

The element in the periodic table with 3 protons is Lithium. This means that the element is lithium ion because it has gained one electron.

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Explanation

Step 1

free body diagram

so, for m1

m1= 10 kg

so,

and for m2

Step 2

now, replace in equaiotn (1) and solve for a

finally, replace in equation (2) to find Tension

I hope this helps you

If we rearrange the circuit so that the inductor and capacitor were connected in series,the impedance would be  Decreased and the resonant frequency would be unchanged.

What is capacitor ?

Frequency is the rate at which something occurs over a particular period of time or in a given sample.

Sol-An LC circuit is made up of an inductor (L) and a capacitor (C). At the resonance condition of the LC circuit, the inductive reactance XL. becomes equal to the capacitive reactance Xc.

It is defined as-

XL= 2πfL

Xc= 1/2πfC

So when reactances are equal we have-

XL=Xc

2πfL= 1/2πfC

f^2=1/4π^2LC

f=1/2π√LC

The resonance condition is the same for both the parallel and series LC circuit, so the resonance frequency will not change.

The impedance of a parallel LC circuit is:

Z(w)= jL w^2-w^2•/w

In a series LC circuit, when w

, the impedance becomes equal to 0.

Therefore the impedance of a series LC circuit will decrease and the resonant frequency will remain the same.

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The recoil speed of the gun is 6.39m/s

What is recoil speed of the gun ?
After firing the bullet, the bullet moves forward with a large momentum and the gun moves backward with an equal momentum. Let m and M be the masses of bullet and gun, respectively. If v and V are the velocities of the bullet and gun, respectively after the firing then:-

0= mv+ MV

Therefore V=-mv/M

The negative sign indicates that the gun moves in a direction to that of
the bullet.
m1v1 = m2v2

m1 = mass of bullet

v1 = velocity of bullet

m2 = mass of gun

v2 = velocity of gun

m1v1=m2v2

0.25*230=9*v2

v2=0.25*230/9 = 6.39m/s

The recoil speed of the gun is 6.39m/s
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The angular acceleration of the beam of length 2 meters and mass 5 kg is 240 radian/s².

The length of the rod is 2 meters, the mass of the rod is 5kg, a force of 200N is applied downward in the east direction while a force of 200N applied upward in west direction.

We know,

That the torque on a body is,

T = Fr

T is torque,

F is the force,

r is the perpendicular distance from the axis of rotation.

So, assuming the centre of the beam as the axis of rotation, the torque on the body is,

T = 200(1)+200(1)

T = 400N-m

We also know,

That torque on the body is,

T = IA

Where I is moment of inertia of the beam,

A is the angular acceleration of the body,

We know, moment of inertia of the beam assuming the centre of the rod as axis of rotation is,

I = MR²/12

M is the mass of the body,

R is the length of the rod,

So,

I = 5(2)²/12

I = 20/12 kg-m²

So, now we can write,

T = 20/12A

As both are value of torque, so,

20/12A = 400

A = 240 radian/s²

The angular acceleration is 240 radian/s².

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Galaxy #2 belongs to  spiral. This is because it has a bulge at the centre, a disk as well as the curved arms. Contains both Young and Old stars - contains gas and dust - contains more red giants and red supergiant's than disk - some regular rotation about centre.

Dark matter is a form of matter thought to account for approximately 85% of the matter in the world. Dark matter consists of particles that do not absorb, reflect or emit light, so they cannot be detected by observing electromagnetic radiation. Dark matter is material that cannot be directly seen. We know  dark matter exists because  it affects objects  we can directly observe.

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The correct answer is option A.

The rocky inner planets are different than the gaseous outer planets because heat from the growing sun allowed rock to mainly form close in.

In our solar system, the inner planets are rocky while the outer planets are in a gaseous state.

Rocky planets are also called terrestrial planets as their outer surface is solid and composed of rocks and metal.

They have large thick gaseous atmospheres which are abundant in gases such as nitrogen, carbon dioxide, and oxygen.

While the outer planets are giant balls of gases that orbit around the sun.

Unlike terrestrial planets, these gaseous planets do not have thick atmospheres and are 2x larger in size than the rocky inner planets.

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Answer:

The answer is 61.45 °C

Explanation:

Clausius-Clapeyron equation:

P2= Normal pressure

T2= Normal boiling point

ln(p2/p1)=−(ΔHv/R)*(1/T2 − 1/T1)

ln(760/190) = –(31400/8.314)*[(1/T2) – (1/298)]

T2 = 334.6 K = 61.45 °C

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