At serve a tennis player aims to hit the ball horizontally.what minimum speed is required for the ball to clear the 0.8m high net about 12m from the server,if the ball is launched from a height of 2m.Where will the ball land if it just clears the net?how long will it be in the air

To determine the minimum speed required for a tennis ball to clear a 0.8-meter high net located 12 meters away, while being launched from a height of 2 meters, we can break this problem down into a few logical steps. We’ll analyze the vertical and horizontal motions separately, applying some basic physics principles along the way.

Understanding the Vertical Motion

First, we need to calculate how long it takes for the ball to fall from its launch height of 2 meters to the height of the net at 0.8 meters. The vertical displacement (h) can be calculated as:

• h = initial height - height of the net = 2 m - 0.8 m = 1.2 m

Using the equation of motion for vertical displacement, we have:

• h = ut + (1/2)gt²

Here, u (initial vertical velocity) is 0 because the ball is hit horizontally, g is the acceleration due to gravity (approximately 9.81 m/s²), and t is the time in seconds. Plugging in the values, we get:

• 1.2 = 0*t + (1/2)(9.81)t²

Simplifying this gives:

• 1.2 = 4.905t²

Now, solving for t:

• t² = 1.2 / 4.905
• t² ≈ 0.244
• t ≈ 0.494 seconds

Calculating the Horizontal Motion

Next, we need to find the horizontal speed required for the ball to travel 12 meters in the time we just calculated (approximately 0.494 seconds). The formula for horizontal distance (d) is:

• d = vt

Rearranging this to solve for v (horizontal speed), we have:

• v = d / t

Substituting the known values:

• v = 12 m / 0.494 s ≈ 24.3 m/s

Where Will the Ball Land?

If the ball just clears the net, it will continue to travel horizontally until it reaches the ground. To find out where it lands, we can use the time of flight we calculated earlier. Since the ball travels horizontally at 24.3 m/s for 0.494 seconds, the horizontal distance it covers after clearing the net can be calculated as:

• Distance = speed × time = 24.3 m/s × 0.494 s ≈ 12 m

Since the ball just clears the net, it will land at a distance of 12 meters from the point of serve, assuming no other forces act on it (like wind resistance).

Summary of Findings

To summarize:

• The minimum speed required for the ball to clear the net is approximately 24.3 m/s.
• The ball will land 12 meters away from the server.
• The time the ball is in the air is approximately 0.494 seconds.

This analysis shows how physics principles can be applied to real-world scenarios like tennis, illustrating the importance of both vertical and horizontal motions in projectile dynamics.