   Chapter 4.9, Problem 69E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# 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?

To determine

The height of cliff.

Explanation

Given data:

Speed is 120fts .

Formula Used:

Write the expression for acceleration function a(t) .

a(t)=v(t) (1)

Here,

v(t) is first derivative of velocity function v(t) .

Write the expression for velocity function v(t) .

v(t)=s(t) (2)

Here,

s(t) is first derivative of displacement function s(t) .

Antiderivative of t is 12t2 and 1 is t .

Calculation:

Consider height of cliff as h and hence the initial displacement is equals to the height of cliff, s(0)=h . The initial velocity of stone is zero, that is v(0)=0 .

The motion of stone is close to ground, so the motion is considered as gravitational constant (g) , which is 32fts2 .

Write the expression for acceleration function (a(t)) .

a(t)=32

Substitute –32 for a(t) in equation (1).

v(t)=32

Antiderivate the expression with respect to t,

v(t)=32t+C (3)

Here,

C is arbitrary constant

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