A place kicker must kick a football from a point 35.0 m (= 38.3 yd) from the goal, and the ball must clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 19.8 m/s at an angle of 45.0o to the horizontal. By how much does the ball clear the crossbar (if in fact it does)? Enter positive values if the ball clears and negative values if it falls below the crossbar. (in m)

Question

A place kicker must kick a football from a point 35.0 m (= 38.3 yd) from the goal, and the ball must clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 19.8 m/s at an angle of 45.0o to the horizontal. By how much does the ball clear the crossbar (if in fact it does)? Enter positive values if the ball clears and negative values if it falls below the crossbar. (in m)
What is the vertical velocity of the ball at the time it reaches the crossbar? Enter positive values if it is still rising and negative values if it is falling. (in m/s)

Steve · Answer

The horizontal and vertical speed are both 19.8/√2 = 14 m/s

At that speed, it takes 35/14 = 2.5 seconds to get to the goal.

The height of the ball is

y = 14t-4.9t^2
y(2.5) = 4.375 m

Looks like it will clear the bar by 1.325 m

I'll let you decide the vertical velocity at t=2.5

v = 14-9.8t