Chapter 3, Problem 85A

a.

To determine

The rock which has greater velocity when they reach the ground.

Answer to Problem 85A

Rock B has greater velocity when it reaches the ground.

Explanation of Solution

Given:

Rock A is dropped from the cliff.

Rock B is thrown upwards from the cliff.

Formula Used:

  $v^2=u^2+2as$

Where,

v is the final velocity

u is the initial velocity.

a is the acceleration

s is the height.

Calculation:

  $v^2=u^2+2as$

  $a=g$ acceleration due to gravity

Let h be the height of the cliff.

For A

  $u=0$

  $v^2=2gh$

  $v_A=\sqrt{2gh}$

For B

Let us assume it reaches the height x from the cliff when thrown upwards.

  $u=0$

Height is $s=h+x$

  $v^2=2g\left(h+x\right)$

  $v_B=\sqrt{2g\left(h+x\right)}$

As $\sqrt{2g\left(h+x\right)}>\sqrt{2gh}$

Rock B has greater velocity when it reaches the ground.

Conclusion:

Rock B has greater velocity when it reaches the ground.

b.

To determine

The rock with greater acceleration.

Explanation of Solution

Introduction:

A free falling motion of a body is one in which gravity is the only force that acts on the body. It is assumed to be an ideal situation such that no other forces act on the body like friction or buoyant forces.

As both the rocks are freely falling bodies, the only forces that act on the body is gravitational force. Therefore, both the bodies experience the same acceleration which is acceleration due to gravity, which is around $9.8{\text{ m/s}}^{-2}$ . For rock B when it thrown up, there is deceleration. When coming down, both the rocks experience an acceleration of $9.8{\text{ m/s}}^{-2}$ .

Conclusion:

Both the rocks have the same acceleration.

c.

To determine

The rock which reaches the ground first.

Explanation of Solution

Introduction:

A free falling motion of a body is one in which gravity is the only force that acts on the body. It is assumed to be an ideal situation such that no other forces act on the body like friction or buoyant forces.

As both the rocks are freely falling bodies, the only forces that act on the body is gravitational force. Therefore, both the bodies experience the same acceleration which is acceleration due to gravity, that is around $9.8{\text{ m/s}}^{-2}$ . As both the rocks experience the same force, Rock A reaches the ground first as it has to travel less distance than Rock B which was thrown upwards.

Conclusion:

Rock A reaches the ground first as it has to travel less distance than Rock B which was thrown upwards.