Question

In soccer, a dropped-ball is a procedure used to restart play if play is stopped and neither team was in clear possession of the ball. The rules state that the referee drops the ball from waist height between opposing players, who can play the ball once it has struck the ground. Howard Webb was an English FIFA referee who refereed the 2010 World Cup Final. With a height of 1.88 m Howard Webb’s waist height would be approximately 1 m. If he were to restart play with a dropped-ball, how long would it take for the ball to strike the ground and how fast would it be going when it struck the ground?

Answer 1

Y = vertical displacement of the ball from waist height to the ground = - 1 m                 (negative sign indicates down direction)

v_o = initial velocity at the top of the waist = 0 m/s

t = time of travel = ?

a = acceleration = - 9.8 m/s²

Using the kinematics equation

Y = v_o t + (0.5) a t²

1 = (0) t + (0.5) (- 9.8) t²

t = 0.45 sec

v = final velocity as it hits the ball

Using the kinematics equation

v = v_o + a t

v = 0 + (- 9.8) (0.45)

v = - 4.41 m/s

so the ball hits the ground with a speed of 4.41 m/s