How would you find initial velocity for this projectile?

Question

This is part of a very long question involving graphs so I won't post the entire thing. I understand most of it, but the final part I couldn't get was finding the initial velocity of a projectile on another planet. I don't know the angle of the projectile. (The x's, o's, and y's are supposed to be subscripts.) I figured out that:
vx = 43.9m/s
projectile starts at 74m
max. height reached= 84.3m
t= 3.5s for the whole trip (until it hits the ground)
a= 24.6m/s^2

I tried using d=voyt + 1/2at^2 and I got voy= 67.14m/s, but when I plugged this in to the pythagorous equation vx^2 + voy^2 = vo^2, I ended up with 80m/s, which isn't correct.
The answer is around 48m/s (give or take a little) but I don't know how to arrive at this. Please help. Any suggestions would be great. Thanks!

Answer 1

I can look at your answer for Voy and see you did something wrong. Not sure what -- at least yet. (I'll try solving as a type)

I'm going to try to solve for Voy using Kinetic and Potential Energy.

Our projectile reached a height of 84.3 m, but that's only 10.3 m above its starting point. I'm going to solve for the difference in energy between starting pointing and max height.

PE=M*A*H
=M*24.6m/s^2 * 10.3m
= M*253.4 m^2/s^2

Now solve for KE (only in y direction) at launch
KE=1/2*M*Voy^2
KE=PE
therefore
1/2M*Voy^2=M*247.2m^2/s^2
Voy^2=2*253.4 m^2/S^2
Voy= 22.5 m/s

Now let's plug it into the quadratic equation
Vo=sqrt (Vox^2+Voy^2)
=sqrt (43.9^2+22.5^2)
=49.3 m/sec

Let's do a double check on the time.
Time up = sqrt (10.3m*2/a) = .838 sec
Time down = sqrt (84.3*2/a)= 2.618
Time total=3.456 Hey, were close

I think, looking at your work that you calculated Voy forgeting that it changed direction at the top. This gave you that absurd number.

Good luck

Answer 2

You should memorize formulas to answer problems like yours.

theta = ?

dx = [vi^2 (sin 2theta) ]/ g

-Remember that vi = vix =vif
-Do some formula tansformation.

(dx)g/ vi^2 = sin 2theta
[(74m)9.8m/s^2]/(43.9m/s)^2 = sin 2theta

(7252 m^2/s^2) / 1927.21m^2/s^2= sin 2theta

3.762952662 = sin 2theta
3.762952662 sin^-1 = 2 theta

ERROR!