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Gary is an outstanding basketball player. He lobs the ball at a height 4 ft above...

Gary is an outstanding basketball player. He lobs the ball at a height 4 ft above the ground and more than halfway across the court at a velocity of 15 m/s at an angle of 60° with respect to the horizontal. The basket is 10 ft off the ground and Gary makes it through the basket. (a) How far from the basket is Gary? (b) There were two possible answers in (a). Only one of them would have scored points. Explain why you chose the answer that you did. (c) What is the maximum height above the ground that the ball reaches?

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Answer #1

Initial horizontal velocity of ball

Initial vertical velocity of ball

Ball is projected at a height of and it reaches the basket at a height of

So distance travelled by ball in vertical direction is

Horizontal distance travelled by ball in a time to reach the basket is -----(1)

Vertical distance travelled by ball in the time to reach the basket is ---(2)

from (1) and (2)

but , and

Gary is at a distance of

b) The ball reaches the height twice in its journey, one while going up () and one while coming down.

In order to score points the ball must reach the basket in the downward direction , which is true when

c)

Maximum height reached by the ball above ground is

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