Question

At what height h above the ground does the projectile have a speed of 0.5v?
Express your answer in terms of v and the magnitude of the acceleration of gravity g.

Answer 1

This question is just looking to to see if you can use your kinematics properly. So we are given some initial v and asked to find h for a final velocity that is one-half the starting velocity. Let's ask ourselves do we have a kinematic equation that deals only with velocities, acceleration and distance? Yes, it's \[v ^{2} = v _{0}^{2} - 2*a*h\] so replace v with .5v_0 you will have \[(\frac{ 1 }{ 2 }*v _{0})^{2} = v _{0}^{2} - 2*a*h\] from here all you do is a little algebra to get h by itself.