A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 27 ft/s.90 ft(a) At what rate is his distance from second base decreasing when he is halfway to first base? (Round your answerto one decimal place.)13X ft/s(b) At what rate is his distance from third base increasing at the same moment? (Round your answer to onedecimal place.)13.416X ft/s

Answered: A baseball diamond is a square with…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 27 ft/s.
90 ft
(a) At what rate is his distance from second base decreasing when he is halfway to first base? (Round your answer
to one decimal place.)
13
X ft/s
(b) At what rate is his distance from third base increasing at the same moment? (Round your answer to one
decimal place.)
13.416
X ft/s

Expert Solution

Step 1

$G i v e n t h a t s i d e o f t h e s q u a r e = 90 f t . r u n s w i t h t h e s p e e d = 27 f t / s . S o l u t i o n : t h e d i s \tan c e c o v e r e d b y t i m e t . s = 27 t d i s \tan c e h a l f o f t h e b a s e, s = 90 / 2 = 45 27 t = 45 t = 45 / 27 a . f r o m t h e s e c o n d b a s e : t h e d i s \tan c e i s g i v e n a s, l = \sqrt{90^{2} + {(90 - 27 t)}^{2}} d i f f r a n c i a t e b o t h s i d e w . r . t t i m e \frac{d l}{d t} = \frac{1}{2 \sqrt{90^{2} + {(90 - 27 t)}^{2}}} \times 2 (90 - 27 t) \times (- 27) p u t t = 45 / 27 \frac{d l}{d t} = \frac{1}{2 \sqrt{90^{2} + {(90 - 27 \times \frac{45}{27})}^{2}}} \times 2 (90 - 27 \times \frac{45}{27}) \times (- 27) \frac{d l}{d t} = \frac{1}{\sqrt{90^{2} + {(45)}^{2}}} \times (45) \times (- 27) \frac{d l}{d t} = - 12.1 f t / s h e n c e, t h e d i s \tan c e f r o m t h e s e c o n d b a s e i s d e c r e a s e s b y 12.1 f t / s$