Sample Question: 4
A 5 kg mass is lifted from the ground to
a height of 10m.
The gravitational potential energy of
the mass is increased approximately
by

There is no such things as an exact measurement there can never be a perfect instrument or measurer.

The term measurement has to do with the process of obtaining the value of a quantity. We know that measurements are done in order to give us an idea of the magnitude of a quantity. In every measurement, there is an instrument that is used for the measurement. For instance, if I want to measure length, I may have to use a meter rule to do it.

Now, there are two ways that error could be introduced into a measurement;

1) By the instrument that is used

2) By the error of the measurer

Hence, there is no such things as an exact measurement there can never be a perfect instrument or measurer.

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Answer:

Velocity is distance + direction / time

so your answer is

75 km north / 1.5 hours

75/1.5  km north/ hours =

50 km / hours north

Answer:

The pelican was travelling at approximately [tex]9.5\; {\rm m\cdot s^{-1}}[/tex] when it dropped the fish.

The fish hit the water at approximately [tex]16\; {\rm m\cdot s^{-1}}[/tex].

(Assumption: air resistance on the fish is negligible; [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex].)

Explanation:

During the descent:

Since acceleration in the vertical direction is constant, make use of the SUVAT equation [tex]x = (1/2)\, a\, t^{2} + v_{0}\, t[/tex] to find the duration [tex]t[/tex] of the descent:

Rearrange this equation to find the duration of the descent, [tex]t[/tex]:

[tex]\begin{aligned} t &= \sqrt{\frac{2\, x}{a}} \\ &= \sqrt{\frac{2 \times 7.8\; {\rm m}}{9.81 \; {\rm m\cdot s^{-2}}} \\ &\approx 1.261\; {\rm s}\end{aligned}[/tex].

The vertical speed of the fish right before impact would be:

[tex]\begin{aligned} v_{y} &= a\, t \\ &\approx 9.81\; {\rm m\cdot s^{-2}} \times 1.261\; {\rm s} \\ &\approx 12.37\; {\rm m\cdot s^{-1}} \end{aligned}[/tex].

In the horizontal direction, the speed of the fish was constant- same as the initial speed of the pelican. The fish travelled a horizontal distance of [tex]x = 12.0 \; {\rm m}[/tex] within the [tex]t \approx 1.26\; {\rm s}[/tex] of the descent. As a result, the horizontal velocity of the fish would be:

[tex]\begin{aligned} v_{x} &= \frac{x}{t}\\ &\approx \frac{12.0\; {\rm m}}{1.261\; {\rm s}} \\ &\approx 9.52\; {\rm m\cdot s^{-1}} \end{aligned}[/tex].

Hence, the initial speed of the pelican would be approximately [tex]9.5\; {\rm m\cdot s^{-1}}[/tex].

Thus, right before impact:

Apply the Pythagorean Theorem to find the overall velocity of the fish at that moment:

[tex]\begin{aligned} v &= \sqrt{{v_{x}}^{2} + {v_{y}}^{2}} \\ &\approx \sqrt{{(9.52\; {\rm m\cdot s^{-1}})}^{2} + {(12.37\; {\rm m\cdot s^{-1}})}^{2}} \\ &\approx 16\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].

In other words, the fish would hit the water at approximately [tex]16\; {\rm m\cdot s^{-1}}[/tex].

Since the graph provided represents voltage and current data for resistor R, the resistance of R is 2.0 Ω

The resistance of a metallic material is its opposition to the flow of electric current.

Resistance is given by R = V/I where

To find the resistance of R, we take the gradient of the graph since reistance R = V/I.

So, the resistance R = ΔV/ΔI where

R = ΔV/ΔI

= (V' - V)/(I' - I)

Taking points from the graph

So, substituting the values of the variables into the equation, we have

R  = (V' - V)/(I' - I)

= (9.0 V - 0 V)/(4.5 A - 0 A)  

= 9.0 V/4.5 A

= 2.0 Ω

So, the resistance of R is 2.0 Ω

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Answer:

Explanation:

the rilation shhip betveen boats annd volummes are ver expennsive

The buoyancy of a boat and the density of the materials used in its construction have an impact on the connection between its volume and the amount of mass it can support before sinking.

Thus, The buoyancy principle asserts that the upward force a fluid (in this case, water) exerts on a submerged or floating item is equal to the weight of the fluid displaced by the object, which is why a boat floats in water.

A boat moves as much water as its own volume while it is submerged in water.

A boat will float if its total weight, including its passengers and cargo, is less than the weight of the water it moves.

Thus, The buoyancy of a boat and the density of the materials used in its construction have an impact on the connection between its volume and the amount of mass it can support before sinking.

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Answer:

200m west

Explanation:

Displacement = v.t where v is the velocity of the object ad t = time

At 50m/hr for 4 hours

Displacement = 50 x 4 = 200m west of origin

Answer:

D

Explanation:

"Simple machines cannot change the amount of work done, but they can reduce the effort force that is required to do the work!"

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red depicts alkali metals, green depicts alkaline earth metals, blue depicts transition metals, and purple depicts inner transition metals.

alkali metal, any of the six chemical elements that make up Group 1 (Ia) of the periodic table—namely, lithium (Li), sodium (Na), potassium (K), rubidium (Rb), cesium (Cs), and francium (Fr).

Group 2A of the periodic table are the alkaline earth metals: beryllium (Be), magnesium (Mg), calcium (Ca), strontium (Sr), barium (Ba), and radium (Ra). They are harder and less reactive than the alkali metals of Group 1A.

transition metal, any of various chemical elements that have valence electrons—i.e., electrons that can participate in the formation of chemical bonds—in two shells instead of only one.

The period 6 inner transition metals (lanthanides) and period 7 are actinides.

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The total displacement of the object was 7.5 meters.

There's a relation between the common movement analysis graphs that we can always use. These relations are the following:

The derivative (slope) of a displacement vs. time graph gives you the function of speed vs. time. Also, when you take the speed vs. time graph and find its derivative, you will get the acceleration function of the observed body.

Now, doing to opposite of derivation (integration), we are able to calculate the displacement of an object when we integrate the function of velocity vs. time. This is not a complicated process when we have a linear function, because integration is just calculating the area under the curve or line of a graph.

In this case, the graph forms a right triangle with the x axis, therefore, we are able to calculate displacement by finding the area under the line of the graph. It could also be made with integration, we are going to do it with both processes as they are both used, and in some cases you have to strictly use one of the 2 in order to get the most precise answers.

When we observe the line, we can crearly tell that the area under the graph constitutes a right triangle. Hence, the area under the graph is given by the following formula:

[tex]A=\frac{bh}{2}[/tex]

Substitute the values and calculate.

(Check attached image 1 to see where the values of b and h are taken from).

[tex]A=\frac{(5)(3)}{2}\\ \\A=7.5[/tex]

Hence, the total displacement of the object was 7.5 meters.

In this method, we'll need to find the equation of the line and then generate and solve a definite integral.

Take 2 points from the line.

(0, 0) and (5, 3).

Find the slope.

Formula: [tex]m=\frac{y_{2} -y_{1} }{x_{2}- x_{1} }[/tex]

[tex]m=\frac{3-0}{5-0}= \\ \\m= \frac{3}{5}[/tex]

Find the equation of the line.

Formula: [tex]y-y_{1} =m(x-x_{1} )[/tex]

[tex]y-(0) =\frac{3}{5} (x-(0) )\\ \\y=\frac{3}{5} x\\ \\[/tex]

Integrate within the interval of interest (from 0 to 5).

[tex]\int\limits^5_0 {(\frac{3}{5} x)} \, dx \\ \\=\frac{3}{5} x^{2} *\frac{1}{2} \\ \\=\frac{3}{10} x^{2} \\\\ (\frac{3}{10} (5)^{2})-(\frac{3}{10} (0)^{2})\\ \\(\frac{3}{10} *25)-(0)\\ \\\frac{75}{10} \\ \\7.5[/tex]

Once again, the total displacement of the object was 7.5 meters.

Answer:

One idea is how, on an astronomical level, the planets can be observed to spread apart continuously.

Explanation:

Throughout various studies, many have observed that the planets continuously grow distant from each other. In fact, it is observed through our technological advances that the very galaxies are slowly drifting apart. Thus, indicating there must have been some big bang to set these galaxies and planets in motion.

The distance travelled in that month is 870.92 miles

We'll begin by calculating the circumference of the tyre. This can be obatined as follow:

C = 2πr

C = 2 × 3.14 × 13

C = 81.64 in

63360 inches = 1 mile

Therefore,

81.64 inches = (81.64 inches × 1 mile) / 63360 inches

81.64 inches = 0.00129 mile

Distance = number × circumference

Distance = 0.00129 × 675135

Distance = 870.92 miles

Thus, the distance travelled in that month is 870.92 miles

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Knowing that Newton's first law is the law of inertia.

The law of inertia helps us when we have problems with bodies that are motionless or moving at constant speed.

The first law tells us that: "A body remains at rest or moves with constant speed if a resultant force equal to zero acts on it."

If the body is at rest or moves with constant speed without acceleration, then the sum of the forces in both the x, y or z axis is equal to zero.

Answer:

God bless you are a hacker the following reas of

Explanation:

God bless you forever to get

(a) Time taken by the stone to fall into the water will be t = 2.99 sec

(b) The speed with which the stone strikes the water will be v=32.91 m/s

(a)

As the stone is kicked horizontally so that the initial velocity of the stone will be [tex]v_{0} = 0[/tex]

For finding the time taken by the stone to fall into the water will be found using the following equation

[tex]y=v_{0}t + \frac{1}{2}at^{2}[/tex]

[tex]y= \frac{1}{2}at^{2}[/tex]

[tex]t=\sqrt{\frac{2y}{a} }[/tex]

[tex]t=\sqrt{\frac{2*(-44 m)}{(-9.8 m/m^{2} )} }[/tex]

[tex]t=2.99 s[/tex]

Time taken by the stone to fall into the water will be t = 2.99 sec

(b)

Since the ball was thrown horizontally, its velocity in the horizontal axis is constant and equal to its beginning velocity.

[tex]v_{0x} = v_{0} = 15 m/s[/tex]

Final velocity at vertical axis is

[tex]v_{y} = v_{0y} + at[/tex]

[tex]v_{y} = at[/tex]

therefore,

time = 2.99 sec

[tex]v_{y} = (-9.8 m/s^{2})(2.99 sec)\\ v_{y} = -29.3 m/s^{}[/tex]

The final velocity is,

[tex]v_{}=\sqrt{v_{0x} ^{2} + v_{y} ^{2} }[/tex]

[tex]v_{}=\sqrt{(15 m/s) ^{2} + (-29.3 m/s) ^{2} }[/tex]

v=32.91 m/s

The speed with which the stone strikes the water will be v=32.91 m/s

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The final speed of the race car, given the data is 49 m/s (Option C)

The acceleration of an object is defined as the rate of change of velocity which time. It is expressed as

a = (v – u) / t

Where

With the above formula, we can determine the final velocity of the car. Details below:

a = (v – u) / t

0.8 = (v – 33) / 20

Cross multiply

v – 33 = 0.8 × 20

v – 33 = 16

Collect like terms

v = 16 + 33

v = 49 m/s

Thus, the final velocity of the car is 49 m/s (Option C)

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The supplied statement states that B has the dimensions L/T².

Measurements like length, width, or height are referred to as dimensions. When you discuss an object or location's dimensions, you're referring to its size and proportions.

Dimensions include length, breadth, and height. One dimension is that of a line, two dimensions are those of a square, and three dimensions are those of a cube (3D).

Just rearranging the equation will get the dimensions.

x = Bt² ----> B= x/t²

Now you are told that x is displacement (L) and t is time (T) so sub these in.

B= L/T² Therefore the dimensions are L/T².

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(i) The angle of inclination of the string to the vertical is 65⁰.

(ii) The tension in the string is determined as 2.11 N.

The angular speed of the string is calculated as follows;

ω = 2πN/60

ω = 2π x 80/60

ω = 8.38 rad/s

v = ωr

v = 8.38 x 0.3 m

v = 2.514 m/s

tanθ = v²/rg

tan θ = (2.514²) / (0.3 x 9.8)

tan θ = 2.15

θ = arc tan(2.15)

θ = 65⁰

T = mv²/r

T = (0.1 x 2.514²) / (0.3)

T = 2.11 N

Thus, the tension in the string is determined as 2.11 N.

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The number of electrons that must be removed from object A and placed on object B is 1.24 * [tex]10^{19}[/tex]

We know that,

E = k [tex]q_{1}[/tex] [tex]q_{2}[/tex] / r²

where,

E = Electrostatic force

k = Coulomb's constant

[tex]q_{1}[/tex], [tex]q_{2}[/tex] = Point charges

r = Distance between two charges

Given that,

[tex]q_{1}[/tex] = 2 + ne C

[tex]q_{2}[/tex] = - 2 - ne C

r = 3 cm

k = 9 * [tex]10^{9}[/tex] N m² / C²

E = - 68 N ( Since it is attractive )

- 68 = 9 * [tex]10^{9}[/tex] ( 2 - ne ) ( - 2 + ne ) / ( 3 * [tex]10^{-2}[/tex] )²

68 * [tex]10^{-4}[/tex] / 3 * [tex]10^{9}[/tex] = ( 2 - ne )²

2.27 * [tex]10^{-12}[/tex] = ( 2 - ne )²

1.5 * [tex]10^{-6}[/tex] = 2 - ne

ne = 1.98

n = 1.98 / 1.6 * [tex]10^{-19}[/tex] = 1.24 * [tex]10^{19}[/tex]

The given problem is an electrostatic attractive force because the two point charges are unlike charges. If the charges are like, then the electrostatic force will be repulsive.

Therefore, the number of electrons that must be removed from object A and placed on object B is 1.24 * [tex]10^{19}[/tex]

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Answer:

[tex]{ \tt{ {v}^{2} = {u}^{2} + 2as}} \\ { \tt{20 = 0 + (2 \times a \times 100)}} \\ { \tt{20 = 200a}} \\ { \tt{a = 0.1 \: {ms}^{ - 2} }}[/tex]

Your weigh on the star methuselah is 38 pounds.

For example, if you weigh 100 pounds on Earth, you would weigh only 38 pounds on Mercury. That's because Mercury weighs less than Earth, and therefore its gravity would pull less on your body.

The element mercury has the atomic number 80 and the symbol Hg. Formerly called hydrargyrum from the Greek words Hydor (water) and Argyros, it's also known as quicksilver (silver). the sole other metallic element that is known to be liquid at standard circumstances for temperature and pressure is the halogen bromine, while metals like cesium, gallium, and rubidium melt just above temperature. Mercury may be a heavy, silvery d-block element.

Worldwide deposits of mercury, primarily as cinnabar, are found (mercuric sulfide). Grinding either synthetic mercuric sulfide or natural cinnabar yields the red color vermilion.

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The resultant displacement of the Polly protractor is 25 km.

The displacement of an object is the change in the position of the object.

The displacement of the Polly protractor is calculated as follows;

d² = 15² + 20²

d = √(15² + 20²)

d = 25 km

Thus, the resultant displacement of the Polly protractor is 25 km.

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The complete question is below:

Find the resultant displacement of the Polly protractor.

Answer:

The mass of the person is 56.83 kg

Explanation:

W= 557 N

We know that acceleration due to gravity (g)= 9.8 m/s^2

Now,

W= mass * acceleration due to gravity

557=m * 9.8

m= 557/9.8

m= 56.83

Answer:

her mass is 55.7 Kg.

Explanation:

Weight = Mass × Acceleration

N =ma [a= g for gravitational force acting down word]

N=Mg

find M so make mass become the subject therefore,

Mass = force / gravitational acceleration [let g=10m/s^2]

m=557 / 10

m= 55.7 kg

The correct answer is 17.12 meters.

S = VoT - (1/2)g[tex]T^2[/tex]

where

S = distance travelled by the body

Vo = initial velocity

T = travel time

g = acceleration due to gravity = 9.8 m/sec^2 (constant)

For the ball,

Sb = 20T - (1/2)(9.8)(  )

and for the stone,

Ss = 24(T - 2) + (1/2)(9.8)(T - 2[tex])^2[/tex]

and for them to pass each other from the release point,

Sb = Ss

and therefore

20T - (1/2)(9.8)[tex]T^2[/tex] = 24(T - 2) - (1/2)(9.8)(T - 2[tex])^2[/tex]

20T - 4.9[tex]T^2[/tex] = 24T - 48 - 4.9([tex]T^2[/tex] - 4T + 4)

20T - 4.9[tex]T^2[/tex] = 24T - 48 - 4.9[tex]T^2[/tex] + 19.6T - 19.6

Combining like terms,

24T + 19.6T - 20T = 48 +19.6

23.6T = 67.6

T = 2.86 sec.

In other words, the stone will pass the ball 2.86 seconds after the ball has been tossed (or 0.86 sec after the stone has been tossed).

Solving for Sb,

Sb = 20(2.86) - (1/2)(9.8)([tex]2.86^2[/tex])

Sb = 17.12 meters -the ball will be passed by the stone at this elevation above the release point. This is the first option in your given choices.

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According to the given statement The dimension of a, b and c is LT⁻² , L and T.

She took exact measurements of the room's length, width, height, and depth in one direction (for example, the distance between the ceiling and the floor of a room). The space was unexpectedly small in all three of its dimensions. Dimensions include length, breadth, and height. One dimension is that of a line, two dimensions are those of a square, and three dimensions are those of a cube (3D).

According to the principle of dimensional homogenity

Dimension of v = dimension of at  =  dimension of  b/t+c

​Dimension of a =   [tex]\frac{[\mathrm{v}]}{[\mathrm{t}]}=\frac{\mathrm{LT}^{-2}}{\mathrm{~T}}=\left[\mathrm{LT}^{-2}\right][/tex]

Dimension of b = [v][t]=[LT −1 T]=[L]

Dimension of c = [t]=[T]

According to the given statement The dimension of a, b and c is LT⁻² , L and T.

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The mass of liquid in the container is 94 grams and the density of the liquid is 0.78 grams/cm³ or 780 Kg/m³.

Given in the question

The volume of the liquid = Volume of the container

                                  =  120 cm³

Total Mass = 145 grams

Mass of the empty Beaker = 51 grams

To find

Mass of the liquid

The density of the liquid

Now,

Total Mass = Mass of LIquid + Mass of the empty Beaker

Mass of LIquid = Total Mass -  Mass of the empty Beaker  

Put in the value, we get

Mass of liquid = 145 - 51 grams

Mass of liquid = 94 grams

Now, Density is the ratio of the mass of the substance and the volume, the substance occupies in the space. It is not a constant value and is variable with the variation in the temperature of the substance. Its S.I. unit is Kg/m³. B ut its other commonly used unit is gram/cm³.

The density of liquid = Mass of the liquid/ Volume of the liquid

Put in the value, we get

The density of the liquid = 94/120  grams/cm³

The density of the liquid = 0.78 grams/cm³ = 780 Kg/m³

Therefore, the mass of liquid in the container is 94 grams and the density of the liquid is 0.78 grams/cm³ or 780 Kg/m³.

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Your question was incomplete. Please find the full content below.

A Measuring Cylinder liquid contains a volume of 120cm³ the liquid was then poured into an empty beaker of mass 51g. The total mass was then found to be 145g . Calculate the mass of the liquid and the density of the liquid.

The final velocity of the bicycle with initial velocity 7.6m/s and acceleration 4.2 m/s² is 28.4 m/s.

What is Velocity?

velocity is defined as the displacement per unit time.

What is Acceleration?

Acceleration is defined as the rate of change of velocity per unit time

i.e.

acceleration = (final velocity (v)-initial velocity)/time taken (t)

given:

initial velocity of the bicycle (u) = 7.6m/s

acceleration of the bicycle (a)=4.2m/s²

displacement of the bicycle=89m

using newtons third law of motion :

v²-u²=2×a×s

using the given value in question we get

v² = (7.6)²+2×4.2×89

v=28.4 m/s

the final velocity of the bicycle with initial velocity 7.6m/s and acceleration 4.2 m/s² is 28.4 m/s.

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The Moment of inertia of the cylinder is equal to 8.82 Kgm².

The propensity of a force to produce or modify the rotational motion of a body is known as torque, also known as moment, or moment of force. It is a force that causes an object to twist or turn. Force and distance are multiplied to calculate torque. It has both a direction and a magnitude because it is a vector quantity. Newton-meters, or N*m, is the torque unit in the SI system.

A spinning object's change in angular velocity per unit of time is expressed quantitatively as angular acceleration, also known as rotational acceleration. It has a vector form.

Given in the question

Torque = 75 Nm

Angular acceleration = 8.5 rad/s²

Torque = Angular acceleration × moment of inertia

Put in the value, we get

Moment of inertia = 75/ 8.5

Moment of inertia = 8.82 Kgm²

So the Moment of inertia of the cylinder is equal to 8.82 Kgm².

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Answer:

Im pretty sure its B

Explanation:

correct me if wrong