A ball is kicked towards goal posts from a position 20m from and directly in front of the posts.

Question 5

A ball is kicked towards goal posts from a position 20m from and directly in front of the posts. The ball takes 0.6s from the time it is kicked to pass over the cross-bar, 2.5m above the ground. The ball is at its maximum height as it passes over the cross-bar. You may ignore air resistance.

 
(a) Calculate the ball’s horizontal component of velocity. 
(b) Calculate the vertical component of the velocity of the ball immediately after it is kicked. 
(c) Determine the magnitude of the initial velocity of the ball immediately after it is kicked.
(d) Determine the angle above the horizontal at which the ball is kicked.

Reference: ???

Solution:

This is a question on projectile motion. The horizontal and vertical component can be considered independently.

(a)

There is no acceleration horizontal (as air resistance is negligible). The ball has a constant horizontal speed.

Speed = distance / time = 20 / 0.6 = 33.3 m s^-1

(b)

Vertically: s = 2.5m                 t = 0.6 s           acceleration a = (-) 9.81 m s^-2 u = ???

Since the ball is at its maximum point, it is n=momentarily at rest: v = 0

v² = u² + 2as

0 = u² + 2 × –9.81 × 2.5          giving u = 7.0 m s^-1

(c)

Component of initial velocity:

The initial velocity v_i is the resultant of the 2 components.

v_i² = (33.3)² + (7.0)²    giving v_i = 34.0 m s^-1

(d)

Angle θ above the horizontal = tan^-1 (7/33.3) = 11.9°