What is this equation?

Question

How would I solve for initial v in terms of theta (angle), D (x displacement), H (y displacement), and g (gravity)

Answer 1

This requires using some of the kinematics equations for physics. First it's important to know that v initial has a horizontal and vertical component. It's also important to know that velocity is change of distance over time and acceleration is change of velocity over time.

The cool thing with gravity (g) is that all things that go up must come down so at some point the speed at the height H is zero so you can figure out how long you're in the air by setting [v (final)]^2 = [v (initial, vertical)]^2 + 2*g (change in time)*displacement in y. Note here gravity pushes down so it's negative here.

0=[v (initial, vertical)]^2-2gH. This means the vertical aspect of v initial is square root of 2gH.

To find the absolute value of initial velocity, it's important to remember that the vertical aspect of velocity is the velocity times sine theta. So divide the vertical aspect of v initial by sine theta to get the initial velocity. Hope that helps!