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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 4.8, Problem 45E

To determine

**To show**: The equation

Expert Solution

The proof of statement

**Given data:**

Initial velocity is

**Formula Used:**

Write the expression for acceleration function

Here,

Write the expression for velocity function

Here,

Antiderivative of

**Calculation:**

Initial velocity is

The motion of stone is close to ground, so the motion is considered as gravitational constant

Write the expression for acceleration function

Substitute

Antiderivate the expression with respect to *t*,

Here,

*C* is arbitrary constant.

Substitute 0 for *t* in equations (3),

Substitute

Substitute
*C* in equation (3),

Substitute

Antiderivate the expression with respect to *t*,

Here,

*D* is arbitrary constant.

Substitute 0 for *t* in equation (5),

Substitute

Substitute
*D* in equation (5),

Apply square on both sides of equation (4).

Add and subtract the term

Substitute

Thus, the proof of statement