By how much vertical distance does the ball clear the crossbar? Answer in units of m

Question

To win the game, a place kicker must kick a football from a point 21 m (22.9656 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 16 m/s at an angle of 55.2 ◦ from the horizontal. The acceleration of gravity is 9.8 m/s 2 .

Answer 1

Projectile motion problem: v = 16 m/s at angle 55.2 degrees; horizontal distance (d_h) is 21 m, vertical height of goal is 3.05 m (d_v)

use angle to get horizontal and vertical components of launch velocity: v_h = 16 cos (55.2) = 9.13 m/s, v_v = 16 sin (55.2) = 13.14 m/s

calculate horizontal travel time to goal = d_h / v_h = 21/9.13 = 2.3 sec

how high is the ball after traveling for 2.3 sec?

height = 0.5gt² + v_vt = 0.5(-9.8)(2.3)² + 13.14(2.3) = -25.9 + 30.2 = 4.3 m

Since the bar is 3.05 m, the ball clears the goal by 4.3 - 3.05 = 1.25 m