Slingshot tricks are *tricks performed using* a slingshot. The slingshot is used to fire a projectile, usually a ball or cube made of rubber, at a target.

A **common trick performed** with the slingshot is *pulling back* the rubber band until it reaches its maximum height, and then firing the projectile at half that height. This is called the U-shot because of the shape of the rubber band as it fires the ball.

To perform a U-shot, you must know how to estimate the speed of your object at half height (1/2)hmax. This article will discuss how to do this!

There are many ways to estimate the speed of an object, but this article will discuss how to do so in the most *accurate way possible*. This article will also explain some concepts related to physics that apply to this topic.

## Calculate the height of the swing

To calculate the height of the swing, you **must first calculate** the length of the swing. This is calculated by doubling the length of the rope and adding half of the diameter of the rope.

For example, if you have a 100-**foot long rope** and a diameter of 4 inches, then your length of swing would be 100 feet + 50 feet (double) + 2 feet (half diameter).

Therefore, your swing would be **102 feet long**. The longer the swing, the higher you will go!

You can also use this formula to calculate other dimensions of your swing, such as width or diameter. Just remember to keep proportions between these dimensions so that your new measurements are actually an upgrade.

## Calculate (1/2)hmax

To calculate the speed of the object at the height of (1/2)hmax, you *must first calculate* how high (1/2)hmax is. You do this by calculating the maximum height of the falling object and dividing that by 2.

Then, you ** must calculate** the velocity of the falling object at half of its maximum height. You do this by taking the velocity of the falling object at its maximum height and dividing it by 2.

Finally, you must calculate (1/2)hmax by taking the average between 1/2hmin and hmax.

This is complicated, so let’s go through each step in more detail. We’ll use some *simpler numbers* to make the calculations easier to understand.

## Find an approximate value for g

To find the approximate value for g, you *must first find* the object’s initial velocity at the height of (1/2)hmax. Then, you **must calculate** the speed at which it will land at hmax.

To do this, use the following formula:

v = sqrt(2gh)

Where v is the velocity, g is the gravitational constant, and h is the height.

Then, take the **square root** of both sides of the equation to get v=g. Divide both sides by h to get v=gh, then replace h with (1/2)hmax to get v=ghmax. The final result is that v=g(1/2)hmax.

## Divide 1 by 2 and multiply by hmax

If you have the height of an object and want to know its maximum speed as it falls, you can use this formula. First, divide 1 by 2 and then multiply by the height of the object.

For example, if an object drops from a height of one meter, its maximum speed will be *one kilometer per hour*. If the object dropped from a hundred meters, then its maximum speed will be **one hundred kilometers per hour**.

This is because when you divide one by two, or 0.5, you get a zero in the numerator. Then you multiply that by the height of the object (100 meters), and you get a new number of *100 kilometers per hour*. This is the object’s maximum speed at that given height.

## Divide 1 by 2 and multiply by (1/2)hmax

To find the speed of an object at half the height of its maximum height, you * must first find* the maximum height of the object. Then, you must find half of that value and subtract it from the original height.

To explain this concept more clearly, let’s use a tennis ball as an example. Suppose a tennis ball was dropped from a height of one meter. To find the speed at which it hits the ground, you must first find the maximum height it reaches before hitting the ground- in this case, one meter.

Then, you **must divide one** by two and multiply by 0.5 meters- in this case, 0.5 meters. The ball will hit the ground with half of its *maximum height left*!

Now, let’s apply this concept to objects that are much taller than a tennis ball- for example, skyscrapers. To find the speed of an object at half the height of its maximum height, first find the maximum height of the object, then divide one by two and multiply by 0.5 times that number.

## Compare your results with those from your classmates

As mentioned before, the final speed of the projectile is determined by the height of launch and type of throw. If the throw is slow or low, then the projectile will land before reaching its maximum height.

If the throw is fast, then the projectile will exceed its maximum height. For both cases, your result should show that the final speed of the projectile is lower than what was predicted by vmax=U√(2gh) .

You can try this experiment yourself with a **rubber ball** and measure its speed and height. You can *also try launching different types* of projectiles to see how their speeds and *heights change*.

## Submit your work

As mentioned before, in order to find the speed at which an object will hit the ground, you need to **know two things**: how tall the object is, and how much time it has to fall.

You have already calculated the height of the object, so now you need to calculate the time it has to fall. To do this, you need to calculate the velocity of the falling object.

The velocity of an object is a measurement of how fast it is moving. You can think of it like traffic speed- if you are walking on a sidewalk outside of a building, you are moving at zero velocity. If you are walking toward a building on the same sidewalk, then you are moving at some level of velocity.

There are three types of velocities: static, dynamic, and kinetic. Static velocity refers to no movement- an object that is sitting still. Dynamic velocity refers to movement, like an object that is falling. Kinetic velocity refers to moving at its **maximum possible speed**– like an object that is rushing down a hill at its peak speed.