How to Calculate the Minimum Speed to Clear a Tennis Net

To calculate the minimum speed needed for a tennis ball to clear a 0.9m high net about 15m from the server, we can use the concept of projectile motion. The ball is launched horizontally, so its initial vertical velocity is zero. By applying equations of motion, we can determine the time it takes for the ball to reach the peak of its trajectory and the time it takes to fall back down to the ground. From there, we can calculate the minimum speed required to clear the net.

Understanding the Calculation Process:

When solving for the minimum speed in this scenario, we need to consider the initial conditions given. The ball is launched from a height of 2.0m, and the net is 0.9m high, positioned 15m from the server. The process involves breaking down the problem into components to determine the minimum speed required.

Using the equation h = ut + 0.5gt^2, where h is the height, u is the initial vertical velocity (which is zero), g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time, we solve for t. Substituting the values, we get: 0.9 = 0 + (0.5)(9.8)t^2. Simplifying, we find t^2 = 0.9 / (0.5)(9.8), and solving for t gives us t ≈ 0.45 seconds.

Utilizing the equation d = vt, where d is the horizontal distance, v is the horizontal velocity, and t is the time, we plug in the values 15m for distance and approximately 0.45s for time. Solving for v, we find v ≈ 33.3 m/s.

Therefore, the minimum speed required for the tennis ball to clear the 0.9m high net positioned about 15m from the server is approximately 33.3 m/s. This calculation considers the launch height and the distance from the server to the net, ensuring the ball successfully clears the obstacle.