Physics question

Question

To win the game, a place kicker must kick a football from a point 28 m (30.6208 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 18 m/s at an angle of 45.6 ◦ from the horizontal. The acceleration of gravity is 9.8 m/s 2 . By how much vertical distance does the ball clear the crossbar? Answer in units of m

Answer 1

d = 28 m

hbar = 3.05

First, find the horizontal (vx) and vertical (vyo) components of the kick velocity (18 m/s) at angle 45.6°.

cos 45.6 = vx/18; vx = 12.6 m/s and sin 45.6 = vyo/18; vyo = 12.9 m/s

The ball move horizontally at a constant 12.6 m/s and takes t = d/v = 28/12.6 = 2.22 s

Now calculate how high the ball will be at 2.22 seconds after the kick as it goes over the bar:

h = xo + vyot + .5gt² = 0 + 12.9(2.22) + .5(-9.8)(2.22)² = 28.7 - 24.2 = 4.5 m

So the ball clears the bar by 4.5 m - 3.05 = 1.45 m