- #1

Maricalue

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I need your help. Is my calculation correct?

1. Homework Statement

1. Homework Statement

We have to build a launcher that will be able to reach a target that is place anywhere in a prism 3m X 3m X 1m. The launcher have to used a golf ball and gravity as source of energy.

I am trying to calculate what we need as energy. :

-We are thinking about using a pendulum.

-We want it to hit the ball in a tube that we could control to adjust the angle of launching.

-We want it to hit the ball in a tube that we could control to adjust the angle of launching.

We know :

-that we have to used 45 degrees to maximize our shot.

-that the ball golf as a coefficient of restitution of 0,83 and a mass of 45,9 g.

-that the longest distance we will have to reach will be at 1,5 m to the left or the right, 1 m from the ground and at 3 m from the launcher.

-that the ball golf as a coefficient of restitution of 0,83 and a mass of 45,9 g.

-that the longest distance we will have to reach will be at 1,5 m to the left or the right, 1 m from the ground and at 3 m from the launcher.

We think of using a mass of 100g for our pendulum.

## Homework Equations

By Pythagoras's theorem, we can calculate the distance we want to reach.

[itex]c^2 = a^2 + b^2[/itex]

Using cinematics equations, I have this :

[itex]x=V_ {xo} * t[/itex]

[itex]y=V_ {yo}* t - \frac{1}{2} g t^2[/itex]

The equation for a inelastic collision is :

[itex]V_ {2}=\frac{C_r m_1 V_1 + m_1 V_1}{m_1 + m_2} [/itex]

For the pendulum, we have the equations of the Law of the Conservation of energy

[itex] \frac{1}{2}mV^2= m g h[/itex]

## The Attempt at a Solution

If we have an angle of 45 degrees, we know that the speed in x and in y will be the same and will be equal to :

[itex]V_ {xo}= V_ {yo} = V sin 45[/itex]

By Pythagora's, we know that we need to reach 3,35 m in X and 1 m in Y.

With the equations of cinematics, I've got :

[itex]V=\frac{x}{\sqrt{(\frac{2(x-y)}{g})}}[/itex]

and that give me [itex]V= 3,42 m/s[/itex]

After that, as I know that the ball golf as a coefficient of restitution of [itex]C_r = 0.83[/itex], I have calculate that I need a speed of [itex]V= 4.2896 m/s[/itex] with the equation of inelastic collision.

Finally, with the equations of the pendulum, I have calculate that I have to have a height of [itex]h = 0.937 m[/itex].Is that correct?

Thank you!

(Sorry if I have made any english errors)