Question

A soccer player is 25 m from the goal and sends a free kick toward the goal which is 2.3 m high

a. the free kick leaves at an angle of 50 degress and has a speed of 15.5 m/s. Does the goalie have to make a save?

b. how fast would the kick have to have been to bounce off the corssbar on its way down?

Answer 1

Time taken by the ball to cover horizontal range

25= 15.5 cos 50*t

t= 2.509 seconds

Height reached by the ball till this time

h= u sin 50*t - 0.5gt^2

h= 15.5 sin 50* 2.509 - 0.5*9.8*2.509*2.509

h= - 1.05 m

Negative sign indicates that ball reach to ground before reaching the goal, so golie have to save the ball.

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b)

Horizontal motion

25= u cos 50*t

ut= 38.9 .. (i)

Vertical motion

2.3= ut*sin 50 - 4.9 t^2

Solving for t

t= 2.37 s

Putting in (i)

u= 16.42 m/s

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