# Tennis: Fan Height Calculation from Ball Speed

• soul5
In summary, the question is asking for the height above the court that a fan catches a tennis ball that bounces upward from the ground with a speed of 16m/s and is caught by the fan with a speed of 12 m/s. The solution involves considering potential gravitational, spring, and kinematic energy at the beginning and end of the motion.
soul5

## Homework Statement

In a tennis match, a player wins a point by hitting the ball sharply to the ground on the opponents side of the net. If the ball bounces upward from the ground with a speed of 16m/s and is caught by a fan with a speed of 12 m/s, how high above the court is the fan?

Don't know.

## The Attempt at a Solution

How do I start this question?

Start with finding out if there is potential gravitational/spring/kinematic enegery at the beginning or at the end.

$$mgh_i + .5m(v_i)^2 + .5k(x_i)^2 = mgh_f + .5m(v_f)^2 + .5k(x_f)^2$$

k i'll do that

## 1. How is fan height calculated from ball speed in tennis?

The fan height is calculated using the formula: fan height = (ball speed)^2 / (2 x acceleration due to gravity). This formula takes into account the time it takes for the ball to travel from the court to the fan, as well as the gravitational pull on the ball.

## 2. Why is fan height important in tennis?

Fan height is important in tennis because it helps players and coaches understand the power and speed of their shots. It also allows for comparison between different players and serves as a measure of a player's strength and skill.

## 3. Does fan height vary for different types of shots in tennis?

Yes, fan height can vary for different types of shots in tennis. For example, a serve will typically have a higher fan height compared to a groundstroke due to the angle and force of the shot.

## 4. Is fan height affected by external factors such as wind?

Yes, external factors such as wind can affect fan height. The wind can either increase or decrease the ball speed, resulting in a higher or lower fan height calculation.

## 5. How accurate is fan height calculation in determining a player's skill level?

The fan height calculation is a useful tool in determining a player's skill level, but it should not be the only factor considered. Factors such as consistency, strategy, and mental toughness also play a significant role in a player's overall performance and should be taken into account.

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