Physics Question (Description)

Question

A place kicker must kick a football from a point 36.0 m from the goal and the ball must clear the horizontal crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 20.0 m/s at an angle of 53° to the horizontal. By how much does the ball clear or fall short above or below the horizontal crossbar?

Answer 1

At initial time t=0

Horizontal component of velocity Vx = V cos 53 = 20 X 0.6018 = 12.036 m/s

Vertical component of velocity Vy = V sin 53 = 20 X 0.7986 = 15.973 m/s

To find height the ball hit the target goal line let us first find time to reach goal line

From mechanics for horizontal distance S

S = Vx X t Given that Sx = 36 m. Therefore t = S / Vx = 36/12.036 = 2.99 s

Now find height H at time 2.99 s

Again from mechanics

H = Vy X t - 1/2 g X t^2 = 15.973 X 2.99 - 1/2 X 9.81 X (2.99) ^2 = 47.759 - 43.851 = 3.907 m

Therefore height above bar = 3.907 - 3.05 = 0.857 m

The ball will cross (above) the bar at a distance of 0.857 m

I hope this helps Habib.

Shailesh K., Senior Math and Physics Instructor