This problem is actually harder than usual:

A ball is shot into the air. At 9.1m above ground, it's x-velocity is 7.6m/s and its y-velocity is 6.1m/s.
I calculated the max-height already. How do I find the initial velocity (components) when it first launched if I don't know the time it took to reach maximum-height?

Question

This problem is actually harder than usual:

A ball is shot into the air. At 9.1m above ground, it's x-velocity is 7.6m/s and its y-velocity is 6.1m/s.
I calculated the max-height already. How do I find the initial velocity (components) when it first launched if I don't know the time it took to reach maximum-height?

mhchen · Answer

This isn't simple speed = distance/time. The equations I'm expected to use is: https://i.ytimg.com/vi/fshSaR5DXVU/hqdefault.jpg Maybe system of equations?

kkutie7 · Answer

so it looks like you need to use the same equation twice:
$$x=x_{0}+v_{0}t+\frac{1}{2}at^{2}$$
$$y=y_{0}+v_{0}t+\frac{1}{2}at^{2}$$

kkutie7 · Answer

oh you don't have acceleration though humm

mhchen · Answer

acceleration in x-direction is 0.
acceleration in y-direction is -9.8

kkutie7 · Answer

I have to go but the idea should be that you solve the equation(s) for what you need in one direction then the other then plug them into each other to find the final answer.

kkutie7 · Answer

* solve one for time including the v0 in the answer and plug it into the other equation

mhchen · Answer

I actually got it. Thanks and medal.