Question

A stone was dropped off a cliff and hit the ground with a speed of 120 ft/s. What is the height of the cliff? 

Answer 1

Step 1 :

The acceleration due to gravity on earth is .

The velocity of the stone can be find , by integrating the acceleration.

Apply integration on each side with t .

The stone is freely falling , so the initial velocity of stone is 0 when t = 0.

Therefore velocity of a stone at time t is  .

Step 2 :

The velocity when it hits the ground is .

Find the time when it reaches the ground.

Negative sign indicates that the stone is falling down.

So the rock reaches the ground at time t = 3.73 sec.

Step 3 :

The position (height) of the stone can be find , by integrating the velocity.

Apply integration on each side with t .

When time t = 0 ,the height of stone is height of the cliff.

is the height of cliff.

When the stone reaches the ground the , the height of the stone is 0.

Substitute t = 3.73 sec and .

The height of the cliff is 224 ft.

Solution :

The height of the cliff is 224 ft.