How to Calculate Catapult Velocity and Maximum Height?

[Cata-tonic]

hi so i had to build a catapult and it's very small, but i need to find the total velocity of the ball upon impact and the maximum height reached. You might need to explain a little bit because I tend to not get things when they are vague so please post more than a formula. Please and thank you so much!

 

[haruspex]

Sounds like you have the catapult and your problem is what to measure in order to be able to estimate these other values, yes?
Are we talking of something hand-held or field artillery?
What mechanism is in use? Need to know how the applied force varies during launch. Knowing that, if you can then measure the peak force you can estimate the launch speed. Everything else follows from that.

 

[the_emi_guy]

I'm thinking if he can measure how far downrange the projectile landed, and the angle with which it left the catapult (90 degrees minus release angle of catapult arm) then we can show him how to compute the other stuff.

 

[jssamp]

That's what I did. Learned tons about ballistics while figuring out formulas to estimate performance. Hardest was the formula to find v_0 from range and launch angle. Cool project, built it mostly out of aluminum, with steel leaf springs to provide the force. Cables from the ends of the spring wrapped around a ratcheting drum. Anyway, if you need some help...

 

[pmacias]

Hello there,

I am happy to assist you with your catapult calculations. To find the total velocity of the ball upon impact, we need to use the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement.

First, we need to determine the initial velocity of the ball. This can be done by measuring the distance the ball travels from the catapult and the time it takes to reach that distance. The initial velocity (u) can then be calculated using the formula u = s/t, where s is the distance and t is the time.

Next, we need to calculate the acceleration of the ball. This can be done by using the formula a = (v-u)/t, where v is the final velocity and t is the time. The final velocity (v) in this case will be zero, as the ball will stop upon impact.

Once we have the initial velocity and acceleration, we can plug them into the first equation to find the final velocity (v) of the ball upon impact.

To find the maximum height reached by the ball, we can use the equation h = u^2/2g, where h is the maximum height, u is the initial velocity, and g is the acceleration due to gravity (9.8 m/s^2). This equation assumes that there is no air resistance.

I hope this explanation helps. If you have any further questions or need clarification, please let me know. Best of luck with your catapult project!