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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?

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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? 
asked Jan 22, 2015 in CALCULUS by anonymous

1 Answer

0 votes

Step 1 :

The acceleration due to gravity on earth is image.

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

image

Apply integration on each side with t .

image

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

image

Therefore velocity of a stone at time t is  image.

Step 2 :

The velocity when it hits the ground is image.

Find the time when it reaches the ground.

image

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.

image

Apply integration on each side with t .

image

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

image

image

image 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 image.

image

The height of the cliff is 224 ft.

Solution :

The height of the cliff is 224 ft.

answered Jan 23, 2015 by yamin_math Mentor

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