Physics project on parabolic motion...?

Question

I've built a trebuchet catapult and have been firing plastacine down the corridor in the name of scinece. I'd like to know any simplish parabolic motion equatins? Oh and they'de be even better if they didn't need a value for initial velocity because I cant figure out how to work that out either. Basically, I'd like to be able to predict where the projectile is going to land before it ever gets there and then to compare that with the actual experimental results that I have. Any help would be greatly appreciated. Thanks all from a very weary A2 level student.

Answer 1

There are a number of ways of figuring this out.

1) calculate the amount of energy stored in your trebuchet in its cocked position. Measure the mass of your projectile. Figure out what velocity it would achieve if all the trebuchet's energy was transferred to it using E = 0.5*(m * V^2) where E = energy, m=projectile mass and V=velocity. re arrange this to give:

v = sqrt ( 2E / m)

Then plug this calculated velocity into your parabola equation. There will be some loss in the system, so you really need step 2 as well.

2: Fire off a few projectiles in your spare time. Measure how far they go then work backwards from the parabola equation to give the original velocity. From this you can calculate the efficiency of energy transfer of your trebuchet too.

I used to love little projects like this at school.
Good luck.
Cheers.

Answer 2

You're going to need the launch velocity.You should be able to get this by experiment.

Set the trebuchet up to launch the projectile at 45 degrees and find the range.

Then the launch velocity is sqrt(Range x g).

The range is

R=(u^2)sin2(theta) over g.

But to do it properly you need degree level maths

Answer 3

Sorry, yet you will might desire to renowned the gap from the floor/floor, the perspective at which you "fling" your merchandise, and the mass of the article flung to boot via fact the preliminary velocity. you are able to be certain this by using using a stopwatch on the huge arm, understanding the gap to the lever that holds your ammunition, the perspective that this arm is going through till it stops; now it is the tangential velocity on the top of the arm. The bag that holds your ammo is likewise a lever arm; understand this distance and use your timer to--looking in easy terms on the bag now--be certain the perspective and time till the bag stops. this is somewhat tough yet I even have completed it particularly properly. a stable polaroid digital camera will aid you be certain the action angles.