On the surface of a planet an object is thrown vertically upward with an initial speed of 60 m/s. use a conservation of energy approach to determine the object's speed when the object is at a quarter of it's maximum height. (assume the planet has no atmosphere)

Question

please help and include the final answer.

Answer 1

a = -g with g unknown

at h = 0, Pe = 0 and Ke = (1/2)m Vi^2
= total energy

at h = Htop , v = o and Pe = m g Htop
= (1/2) m Vi^2
so
Htop = Vi^2/2g

at h = Htop/4
Pe = m g (Htop/4) = m Vi^2/8
total energy still = m Vi^2/2
so Ke = (3/4) (1/2)m Vi^2
so it still has (3/4) of initial Ke
v^2 = (3/4)Vi^2
v = (sqrt 3) (60)/2