A place-kicker must kick a football from a point 36.0 m (about 40 yards) from th

Question

A place-kicker must kick a football from a point 36.0 m (about 40 yards) from the goal. 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 20.6 m/s at an angle of 52.0° to the horizontal. (a) By how much does the ball clear or fall short (vertically) of clearing the crossbar? (Enter a negative answer if it falls short.)

(b) Does the ball approach the crossbar (and cross above or beneath it) while still rising or while falling?   

Explanation / Answer

initial velocity vo = 20.6 m/s

along horizantal

vox = vo*cos52

x = vox*t

t = x / vox..........(1)

for x = 36 m

t = 36/(20.6*cos52) = 2.84 s

along vertical

voy = vo*sin52

y = voy*t + 0.5*ay*t^2

y = (20.6*sin52*2.84)-(0.5*9.8*2.84^2)

y = 6.58 m

y > h ( height of the cross bar

(a)

y-h = 6.58 - 3.05 = 3.03 m <<------answer

(b)

for t = 2.84

vy = voy + ay*t

vy = (20.6*sin52)-(9.8*2.84) = -11.6 m/s

the vy is negative

the ballis falling while it approaches the cross bar

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