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3 years ago

5

A stone is dropped from a cliff and falls 9.44 meters. What is the speed of the stone when it reaches the ground?

1 answer:

Lunna [17]3 years ago

3 0

Answer:

option A

Explanation:

given,

height of the drop of stone = 9.44 m

speed of the stone = ?

As the stone is dropped the energy of the stone will be conserved.

using conservation of energy.

Potential energy = Kinetic energy

$m g h = \dfrac{1}{2} m v^2$

$v = \sqrt{2gh}$

$v = \sqrt{2\times 9.8 \times 9.44}$

$v = \sqrt{185.024}$

v = 13.60 m/s

Hence, the correct answer is option A

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Bingel [31]

Answer:

The rate of change of height with respect to time is -10.64 feet/sec

Explanation:

Given that,

There are three lines, so you can calculate three different values of the function at one time.

The function f(t) represents the height in feet of a ball thrown into the air, t seconds after it has been thrown.

Given table is,

Time t = 0, 1, 1,02

Function is, $F(t)=-3.053113177191196\times10^{-18},6.000000000000134, 6.41760000000015$

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Using equation of motion

$h=h_{0}+ut-\dfrac{1}{2}gt^2$

Where, h₀ = initial height

u = initial velocity

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g = acceleration due to gravity

At t = 0,

Put the value into the formula

$-3.053113177191196\times10^{-18}=h_{0}+0-0$

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Using equation of motion

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$6.000000000000134=-3.053113177191196\times10^{-18}+u-\dfrac{1}{2}\times32$

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Velocity is the rate of change of height with respect to time

So, velocity at 1.02 sec is given

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$h=ut-\dfrac{1}{2}gt^2$

On differentiating w.r.to t

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3 years ago

A 20-kg block is held at rest on the inclined slope by a peg. A 2-kg pendulum starts at rest in a horizontal position when it is

gregori [183]

Complete Question

The diagram of this question is shown on the first uploaded image

Answer:

The distance the block slides before stopping is $d = 0.313 \ m$

Explanation:

The free body diagram for the diagram in the question is shown

From the diagram the angle is $\theta = 25 ^o$

$sin \theta = \frac{h}{d}$

Where $h = h_b - h_a$

So $d sin \theta = h_b - h_a$

From the question we are told that

The mass of the block is $m = 20 \ kg$

The mass of the pendulum is $m_p = 2 \ kg$

The velocity of the pendulum at the bottom of swing is $v_p = 15 m/s$

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The coefficient of kinetic friction is $\mu _k = 0.5$

The velocity of the block after the impact is mathematically represented as

$v_2 f = \frac{m_b - em_p}{m_b + m_p} * v_2 i + \frac{[1 + e] m_1}{m_1 + m_2 } v_p$

Where $v_2 i$ is the velocity of the block before collision which is 0

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Substituting value

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The energy at point a = energy at point b

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Where

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$PE_A = m_b gh_a$ = 0 at the bottom

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$K_A = \frac{1}{2} m_b * v_2f^2$

$PE_B$ is the potential energy at B which is mathematically represented as

$PE_B = m_b gh$

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