A placekicker must kick a football from a point 36.0 m (about 40 yards) from the

Question

A placekicker must kick a football from a point 36.0 m (about 40 yards) from the goal, and half the crowd hopes the ball will clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 21.0 m/s at an angle of 45.0° to the horizontal.

(a) By how much does the ball clear or fall short of clearing or fall short of clearing the crossbar? (Enter a negative answer if it falls short.)
??? m
(b) Does the ball approach the crossbar while still rising or while falling?

???    

Explanation / Answer

time taken to travel 36 is t = S/vcos theta   = 36/(21cos45)

t = 2.42 secs

Vertical height travelled during this time is H = U sin theta t - 0.5 gt^2

H = (21sin45 * 2.42) - (4.9*2.42^2)

H = 7.23 m

since 7.23 is more than 3.05 m, the ball is above the cross bar by a height of (7.23- 3.05) = 4.18 m

The velocity at the end of 2.42 secs is

v = u –gt = (21 sin 45) – (9.8*2.42)

V = -8.86 m/s

The negative sign shows that the ball is falling down, while approaching the cross bar.

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