help help please, physics?

Question

A ball is thrown straight up into the air with an initial speed v, and reaches a maximum height h. If the ball is again thrown vertically, but this time with a speed of v/2, what maximum height will it attain?

Answer 1

The relation between initial speed and height is obtain by equating the energy values

0.5*m*v^2 = m*g*h

Therefore h = (0.5*v^2)/g.

The height is proportional to v^2, so the height will drop by a factor of 4 (h/4)