physics

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i have to build a catapult that will fire a projectile that will pass a 1m tall wall 1 m away from starting point and land in a target 1 m away from the wall. the catapult cant be more than 23cm high.

I'm having some problems here with this

for simpicity issues
i said launch at .2m off the ground at origin and reach a height of 1.1m at 1m away just incase something screws up.

I need to find the
Vi
Vyi
Vxi

and am having some trouble and don't know what angle is best so that less speed is needed for this to work

• physics -

You have selected 0.2 m for the initial height and 1.1 m for the maximum height. That allows you to calculate the time the projectile must spend coming down (t2) and going up (t1).
(g/2) t2^2 = 1.1 m
t2 = 0.474 s
(g/2) t1^2 = 0.9 m
t1 = 0.429 s
Initial y component of velocity:
Vyi = g*t1 = 4.204 m/s

Total time of flight = 0.903 s
Vxi*0.903 s = 2.0 m
Vxi = 2.214 m/s

Vi = sqrt(Vxi^2 + Vyi^2) = 4.751 m/s

These two components determine the initial launch angle as
arctan(Vyi/Vxi) = 62.2 degrees