In a serve, a tennis player hits the ball horizontally. Neglect the effects of air resistance and the diameter of the ball. What minimum speed is required for the ball to clear the .9m net 15.0 m from the servier if the ball is launched from a height of 2.5 m? Where will the ball land if it just clears the net?

Question

In a serve, a tennis player hits the ball horizontally. Neglect the effects of air resistance and the diameter of the ball. What minimum speed is required for the ball to clear the .9m net 15.0 m from the servier if the ball is launched from a height of 2.5 m? Where will the ball land if it just clears the net?

Answer 1

Can you explain

Answer 2

To find the minimum speed required for the ball to clear the net, we can use the principles of projectile motion.

First, let's consider the vertical motion of the ball. The ball is launched from a height of 2.5 m and it needs to clear the 0.9 m net. So, the vertical displacement of the ball is given by:

Vertical displacement = 2.5 m + 0.9 m = 3.4 m

Since we neglect air resistance, the vertical motion of the ball is governed by the equation of motion:

Vertical displacement = Initial vertical velocity * Time - (1/2) * gravitational acceleration * Time^2

Here, the initial vertical velocity is 0, as the ball is launched horizontally. The gravitational acceleration can be taken as -9.8 m/s^2 (negative sign indicates motion against gravity). We can rearrange the equation to solve for time:

Time = sqrt((2 * Vertical displacement) / gravitational acceleration)

Plugging in the values, we get:

Time = sqrt((2 * 3.4 m) / 9.8 m/s^2) ≈ 0.824 s

Now, let's consider the horizontal motion of the ball. The horizontal distance covered by the ball is 15.0 m, and the time taken (as calculated above) is 0.824 s. We can use the equation for horizontal distance to find the minimum required horizontal velocity:

Horizontal distance = Horizontal velocity * Time

Rearranging the equation, we get:

Horizontal velocity = Horizontal distance / Time

Plugging in the values, we get:

Horizontal velocity = 15.0 m / 0.824 s ≈ 18.20 m/s

So, the minimum speed required for the ball to clear the net is approximately 18.20 m/s.

To find where the ball will land if it just clears the net, we can use the same horizontal velocity:

Horizontal distance = Horizontal velocity * Time

Plugging in the values, we get:

Horizontal distance = 18.20 m/s * 0.824 s ≈ 15.00 m

So, the ball will land approximately 15.00 m from the server if it just clears the net.