To win the game, a place kicker must kick a football from 30m from the goal, and the ball must clear the crossbar which is 3.05 m high. When kicked, the ball leaves the ground with the speed of 19 m/s at the angle of 37.2° from the horizontal. Acceleration of gravity is 9.8 m/s^2 How much vertical distance does the ball clear the crossbar?

Explanation:

Ignore air resistance

The horizontal velocity is

vx =19cos37.2 = 15.134 m/s

The ball travels 30 m in a time of

30 / 15.134 = 1.982 s

In that time, the ball will be at an altitude of

s = vy₀t + ½at²

s = 19sin37.2(1.982) + ½(-9.8)1.982² = 3.5137... m

so the ball clears the bar by

h = 3.5137 - 3.05 = 0.4637... = 0.46 m

which piece of furniture will have the most inertia and give the furniture movers the most difficulty in moving?  

answer

a 75kg dining table

the maxium height is 34m/s