A tennis ball located 2 m height is hit by a player with his racket. The ball shoots out horizontally with a velocity of 30 m/s. Answer the following questions:
a) How long does the ball takes to hit the ground?
b) What is the angle of the velocity vector with the x-axis at the time the ball reaches the ground?
c) If before being hit, the ball is 5 meters away from the net, how high does the ball pass above the net?
The ball will reach the ground when the y-coordinate of its position is 0 (y=0). According to the equations of horizontal launch:
To calculate the angle that the velocity vector forms with the x-axis, we will use the following expression:
To solve it, we will calculate vx and vy:
Once we have the velocity data, we can get the angle:
To calculate the height at which the ball will pass above the net, first, we must know when it crosses above the net. To do so, knowing that the ball is 5 m away from the net and moves with a u.r.m. at 30 m/s:
At that time the ball will be just over the net, so we simply calculate its position and we would have solved the problem: