Catapult lab help needed please

[alli66]

[Note from mentor: This was originally posted in a non-homework forum, therefore it does not use the homework template.]

we did a lab on catapult but I'm having trouble figuring out the math? i calculated the hangtime, but all i did was take the original time and divide it by 2, is that right?
QUESTIONS:
1) how long did it take to reach peak height?
2) what is the projectiles initial vel in the x and y direction?
3) what was the initial vel.?
4) what was the peak height?
5) how much PE did the ball have at the peak height?use h from #4
6) what's the KE of the ball at the launch? use vi from #3
7) how fast is the ball moving at the peak height?use conservation of energy
8 )what was the elastic P.E of the catapult?
9) what was the spring constant?
10) how much work was done by gravity on the ball?

DATA:
- catapult launch angle 70 degrees
- length of armature = 28cm
- elastic band length before= .875in
- elastic band length after= 2.75 in
- mass of ball= 18.75 g

launch distance: trial 1: 12.85m, trial 2: 3.09m, trial 3: 3.15m, avg of the 3= 3.03 m
hang time: original time divided by 2 to get hang time? that's what i did but i think its wrong: trial 1: 1.60s/2 =.8 sec, trial 2: 1.65 sec/2= .825, trial 3: 1.71/2=.855s,, avg of 3 hangtimes= .8266secs

 

[scottdave]

In your handwritten data sheet it is 2.85 meters on trial#1, not 12.85 as you typed. I was wondering how you came up with that average.
The definition of hang time, is the total amount of time in the air ( https://en.wikipedia.org/wiki/Hang_time ) That is from time it leaves the catapult until it touches the ground. So hang time would be the total time. But did your teacher define it differently? What do you mean by original time?

With no air resistance, and if launched from ground level, the projectile will spend half of the time going up, and half going down, so your time to peak (in that situation) is half of the total time. So there is going to be air resistance, but those effects may be minimal if the projectile is smooth shaped and has "enough" mass, and the air is calm. So was it launched from ground level, where the distance up equals the distance back down? If the catapult is "short enough" then you could approximate that it was launched from ground level. That may be what you have to do for this particular lab.

 

[scottdave]

You can find the initial vertical velocity using equations of motion ( https://en.wikipedia.org/wiki/Equations_of_motion#Uniform_acceleration ).