PRECALCULUS:...COMMON CORE ED.-W/ACCESS
10th Edition
ISBN: 9780134781839
Author: Demana
Publisher: PEARSON
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Expert Solution & Answer
Chapter 6.3, Problem 43E
Solution
a)
To find: how many seconds after the ball is hit does it hit the wall.
The ball will hit the wall approximately in 2.8 seconds.
Given information:
x=(150cos18°)t and y=−16t2+(150sin18°)t+3 .
Formula used:
x=(v0cosθ°)t and y=−16t2+(v0sinθ°)t+h .
Calculation:
Substitute 400 for x in x=(150cos18°)t .
400=(150cos18°)t400=(150)(0.9511)t400=142.665t400142.665=tt≈2.8
Hence, the ball will hit the wall approximately in 2.8 seconds.
b)
To find: how high up the wall does the ball hit.
The ball will hit the wall at 7.34 ft.
Given information:
x=(150cos18°)t and y=−16t2+(150sin18°)t+3 .
Formula used:
x=(v0cosθ°)t and y=−16t2+(v0sinθ°)t+h .
Calculation:
Substitute 2.8 for t in y=−16t2+(150sin18°)t+3 .
y=−16(2.8)2+(150sin18°)2.8+3y=−16(7.84)+150(0.309)(2.8)+3=−125.44+129.78+3=7.34
Hence, the ball will hit the wall at 7.34 ft.
c)
To explain: why Kevin’s hit might me caught by an outfielder and also explain why his would probably be not caught if it were hit at an angle of 20° with the horizontal.
The outfielder would not be able to catch a ball which would be at a height of 21.2 ft when hit with an angle of 20° .
Given information:
x=(150cos18°)t and y=−16t2+(150sin18°)t+3 .
Formula used:
x=(v0cosθ°)t and y=−16t2+(v0sinθ°)t+h .
Calculation:
Substitute 2.8 for t and 18° for θ in y=−16t2+(150sinθ)t+3 .
y=−16(2.7)2+(150sin18°)2.7+3=−16(7.29)+150(0.309)(2.7)+3=−121+127.46+3=7.35
Since the height of the ball is 7.35 feet at 2.8 seconds the outfielder might be able to catch it.
Substitute 2.8 for t and 20° for θ in y=−16t2+(150sinθ)t+3 .
y=−16(2.8)2+(150sin20°)2.8+3=−16(7.84)+150(0.342)(2.8)+3=−125.44+143.64+3=21.2
Hence, the outfielder would not be able to catch a ball which would be at a height of 21.2 ft when hit with an angle of 20° .
Chapter 6 Solutions
PRECALCULUS:...COMMON CORE ED.-W/ACCESS
Ch. 6.1 - Prob. 1QRCh. 6.1 - Prob. 2QRCh. 6.1 - Prob. 3QRCh. 6.1 - Prob. 4QRCh. 6.1 - Prob. 5QRCh. 6.1 - Prob. 6QRCh. 6.1 - Prob. 7QRCh. 6.1 - Prob. 8QRCh. 6.1 - Prob. 9QRCh. 6.1 - Prob. 10QR
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Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning