physics question

Question

During a game, a soccer player kicks the ball from the field. The soccer ball has an initial speed of 19.4 m/s at an upward angle of 45°. A player from the opposing team 55 m away in the direction of the kick starts running to meet the ball at the instant it is kicked.

Determine the average speed this player must have in order to reach the ball just before it hits the ground?

Answer 1

Resolve the velocity ball is kicked into horizontal and vertical components.

Horizontal component = 19.4 * cos(45) = 13.72 m / sec

Vertical component = 19.4 * sin(45) = 13.72 m / sec

To find out how long ball is in the air:

s = vertical component * time - 0.5 * 9.8 * time * time

set displacement (s) = 0,

0 = 13.72 * time - 4.9 * time * time

time = 13.72 / 4.9 = 2.8 seconds ball is in the air.

To find horizontal distance ball travels = horizontal velocity * time = 13.72 * 2.8 = 38.416

Therefore opposing player must travel 55 - 38..416 meters to meet ball when it lands = 16.584 meters

Velocity player must run is 16.584 / 2.8 = 5.92 m / s