How to Calculate the Speed of a Tennis Ball Leaving the Launcher

Decompose the Velocity

Firstly, decompose the velocity of the tennis ball into its horizontal and vertical components. The vertical component is given by V₀⋅sinθ, where V₀ is the initial speed and θ is the launch angle. The horizontal component is given by V₀⋅cosθ.

Utilize Equations of Motion

Since we are neglecting air resistance, we can utilize the equations of motion to find the initial speed. The equations help in determining the relationship between distance, time, and acceleration.

Calculate Time

Since the ball lands at the same height above the ground from where it was launched, the time taken to reach the maximum height and to return to the ground is the same. Use the equations to calculate the time taken to reach the maximum height.

Solve for Initial Speed

Substitute the calculated time back into the equation involving the initial speed, launch angle, and distance. Solve for the initial speed of the tennis ball as it leaves the launcher.

Check Your Answer

After calculating the initial speed, double-check your calculations to ensure accuracy. Double-checking helps in confirming the correct speed of the tennis ball as it leaves the launcher.