# What is the mathematical relationship between the drop height and the bounce height of a tennis ball?

Table of Contents

## What is the mathematical relationship between the drop height and the bounce height of a tennis ball?

Conclusion. Drop height and bounce height are directly proportional. The constant of proportionality is distance (blocks). There is a 32.34 % difference from mean when compared to another group.

## What is the equation for rebound ratio?

Just using these two measurements, I can find the rebound ratio. Using the geometric sequence formula, we have 111=200(r)(2−1). 200 represents the initial height, and (2, 111) represents the second height after the first bounce at 111 cm.

## What mathematical equation did you use to get the max height for each bounce?

Quadratic Model: Height of Single Bounce Using a formula from physics that relates an object’s height to the length of time it has been falling, h = 16t 2 (16 is half the rate of acceleration due to gravity in feet per second squared), it can be determined how long it takes to fall from each height.

## How do you measure the rebound height of a ball?

The test is conducted with an electromagnetic or vacuum release mechanism which releases a soccer ball from a height of 2 meters. From that the height of the rebound is measured by recording the sound of the first and second bounce. The time between the first and second bounce is measured.

## How do you calculate average bounce height?

MATERIALS: Tennis ball, meter stick. Step 1: Drop the ball from 100 cm. Measure how high it rebounds after the first bounce. Repeat three times, then find the average height after one bounce.

## What is the relationship between drop height and bounce height?

The relationship between drop height and bounce height is only linear for small drop heights. Once a ball reaches a certain height, the bounce height will begin to level off because the ball will reach its terminal velocity.

## What affects the bounce height of a ball?

The combination of the material properties of a ball (surface textures, actual materials, amount of air, hardness/ softness, and so on) affects the height of its bounce.

## Why does the height of a bouncing ball decreases?

During a collision, some of the ball’s energy is converted into heat. As no energy is added to the ball, the ball bounces back with less kinetic energy and cannot reach quite the same height. It reaches way higher than from the height it was released.

## How does a surface affect the bounce height of a ball?

When a basketball bounces off of a surface, some of its energy is absorbed by that surface. A hard surface, such as concrete, absorbs less energy compared with a soft surface, such as a carpeted floor. The more energy absorbed by the surface, the less that remains in the ball for it to bounce.

## Which surface is best to bounce a ball on?

The harder the court surface is the more energy a dropped ball retains and the higher it rebounds. A basketball bounces pretty well on hardwood, but even better on concrete. But, if the floor is too hard, it can lead to serious player injuries.

## Does density affect bounce height?

The density of a ball may be a component of how high it bounces, but it is not the sole determining factor.

## Does the height of a tennis ball drop affect the height of the bounce?

You’ve probably noticed that if you drop even the bounciest of tennis balls from a height, it never bounces back higher than where it started. When you drop the ball, gravity pulls it down and it picks up speed. As the squashed ball springs back to its original shape, it pushes on the floor and the floor pushes back.

## Does drop height affect bounce efficiency?

The efficiency of a ball can be calculated by dropping and measuring the height of the bounce. The higher the bounce, the more efficient the ball is. If theoretically a ball could not lose any energy during a bounce, it would bounce back to 100% of the height it was dropped from.

## Why doesn’t a ball bounce back to its original height?

This elastic potential energy is why the ball is able to bounce, or rebound. After the ball rebounds, the elastic potential energy is transformed into kinetic energy, but it will never possess as much kinetic energy as during its original fall. The ball will never be able to rebound to its original height.

## How much energy is lost when a ball bounces?

For example, if a ball bounces 80% of its height on each bounce, then the ball is losing 20% of its energy on each bounce. The time of each bounce is about 90% of the time of the previous bounce, the ball slows down about 10% each bounce, and about 10% of the linear momentum is lost at each bounce.

## Why is it impossible for a ball to be 100% efficient?

No machine is free from the effects of gravity, and even with wonderful lubrication, friction always exists. The energy a machine produces is always less than the energy put into it (energy input). That is why 100% efficiency in machines shall not be possible.

## Is 100 energy efficiency possible?

Originally Answered: Is it possible to achieve 100% energy efficiency? No its not. According to thumb rule, energy efficiency can only be 1 (100%) when output is equal to input (all work done convert into energy) which is not possible because of various factors like heat loss, friction loss etc.

## Is the Carnot cycle 100% efficient?

The efficiency of Carnot engine = 1 – (sink temperature / source temperature). As per the Kelvin Planck statement no engine has 100 % efficiency. Sink temperature will always be less than that of source temperature. Thus efficiency of Carnot cycle becomes less than 100 %.

## What is the formula for efficiency?

Efficiency is often measured as the ratio of useful output to total input, which can be expressed with the mathematical formula r=P/C, where P is the amount of useful output (“product”) produced per the amount C (“cost”) of resources consumed.

## Which energy has lowest efficiency?

For this reason, the efficiency of usable energy for the least efficient source of energy — coal — comes in at a meager 29% of its original energy value. Wind, on the other hand, provides an impressive 1,164% of its original input of energy!

## What is the most powerful energy source?

Nuclear Has The Highest Capacity Factor As you can see, nuclear energy has by far the highest capacity factor of any other energy source. This basically means nuclear power plants are producing maximum power more than 93% of the time during the year.

## What is the most efficient way to produce electricity?

Although there are many types of energy, the most efficient forms are renewable: hydro-thermal, tidal, wind, and solar. Solar energy has been proven to be the most efficient and effective among renewable energy sources for home and commercial use.

## What are 5 advantages of hydropower?

Advantages of hydroelectric energy

- Renewable. Hydroelectric energy is classified as a renewable energy source because it is powered by water, and water is a naturally replenishing resource.
- Low emissions.
- Reliable.
- Safe.
- Environmental consequences.
- Expensive to build.
- Drought potential.
- Limited reservoirs.

## Why hydropower is not clean energy?

Hydropower dams and reservoirs emit methane, a greenhouse gas that is 20 times more potent than carbon dioxide. These emissions are caused by the decomposition of organic vegetation flowing into the water as the reservoir levels fluctuate, and as rivers and floodplains are flooded each year.

## Why isn’t hydropower used more?

Hydropower fell out of favor in the ’90s because of the harm it can cause to communities and ecosystems. However, a recent push from the World Bank for more hydro projects worldwide, especially in developing countries, could lead to a resurgence of hydropower plants, the Washington Post reports.

## What are the pros of hydropower?

Pros of Hydroelectric Energy

- It’s Good for the Environment.
- It’s a Renewable Resource.
- It’s Reliable and Highly Efficient.
- It’s Flexible.
- It’s Safe.
- It’s Economical.
- It’s Great for Recreational Use.
- It’s a Fundamental Vehicle for Development.