Workout initial velocity of projectile without knowing launch angle

Question

I am trying to work out the speed of a tennis serve. I know the following: X Distance: 18m, Time: 0.5s, g: 9.8, Launch height: 3m. Is it possible to work out the initial velocity of the serve considering that I don't know the launch angle? Many thanks, George

Answer 1

Hint:

The initial velocity is mate up of two components: the velocity in the $x$ (horizontal) direction and the velocity in the $y$ (vertical) direction.

• You can calculate the first using the time and distance travelled (as it remains constant throughout the flight).
• You can calculate the second using the time it takes for the ball to fall and the height from which it fell. The speed in the vertical direction increases with time.