Maximum Height
Once the ball leaves the racquet, it becomes a projectile. The ball is initially hit at an angle of 18º above the horizontal, and therefore the ball starts to rise. However, since the ball still has gravity acting upon it, at a certain point it will lose all upwards (positive) velocity and start to gain downward (negative) velocity, which means it will start to fall. If the path of the ball were shown, it would form an arc. Instantaneously, at the top of the arc, the ball has a vertical velocity of exactly 0 m/s, which means that its only motion is horizontal. After that point, the ball is falling. It is using this exact point that we can find the maximum height of the ball. First, we must use the equation involving displacement, initial velocity and final velocity, and acceleration. With this, we can find the maximum height of the ball above the contact point:
Therefore the distance from the contact point to the maximum height is 1.47m [up].
We must then find the distance from the contact point to the ground, and add that to the distance from the contact point to the maximum height:
We must then find the distance from the contact point to the ground, and add that to the distance from the contact point to the maximum height:
Therefore the distance from the contact point to the ground is 0.76m and the maximum height is 2.2m
Trajectory and Optimal Angles
If you were to trace the trajectory of the ball, it would form an arc. The reason it needs to form and arc is so that is able to make it over the net. We know that the maximum height of the ball and also the distance the ball travels depends on the angle the ball is hit at. If the ball were hit at an angle below the horizontal from its initial height of 0.76m, it would hit the ground before it even got to the net. If the ball were hit at a lower angle but still above the horizontal, it might hit the net, since it needs to rise at least 0.31m from the contact point to clear it, and such an angle might not cause the ball to rise this much. If the ball were hit at an angle closer to 45º with the same force, it might go out of bounds because the distance would be far greater. At an angle closer to 90º, the ball would go high, but might not have the distance to make it over the net, which means it would still not be a good shot. an angle of around 20º will create the optimum shot, since the ball will clear the net, and it will also land close to the baseline, but will still be in the court.