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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 24 ft/s.

(a) At what rate is his distance from second base decreasing when he is halfway to first base?

(b) At what rate is his distance from third base increasing at the same moment?

Chapter 2.8, Problem 20E, A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base

To determine

a)

To Find:

The rate at which his distance from second base is decreasing.

Explanation

1. Concept:

We can plot the figure from the given situation and the figure is as shown below.

Let x = distance from runner to first base and y = distance from runner to second base.

We can apply the Pythagorean Theorem on the triangle and then apply the differentiation rules to find the rate.

2. Formula:

i. Pythagorean Theorem:

Hypoteneous2=Sum of squares of perpendicular sides

ii. Power rule of differentiation:

ddxxn=n*xn-1

 iii. Chain rule of differentiation:

ddtfx=ddxfx*dxdt

3. Given:

x = 45 ft.,dxdt=24 ft/s

4. Calculations:

By Pythagorean Theorem,

x2+902= y2

Differentiate it with respect to t

To determine

b)

To find:

The rate at which distance from the third base is increasing at the same moment.

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