An object is on the ground and launched up into the air at a velocity of 30 m/s. What would be the object's potential energy at its maximum height?

Hello!

The only force acting on this projectile object is the gravity force `mg.` By Newton's Second law, an object's motion is uniformly accelerated (or we can say "decelerated") from the start to the point of maximum height.

The velocity will be `V(t)=V_0-g t,` where `V_0` is the initial speed, and the height will be `H(t)=V_0 t - (g t^2)/2.` Therefore the time of maximum height will be `t_1=V_0/g` and the height itself will be `V_0^2/(2g).`

The potential energy will be `mgh=(m V_0^2 )/2.` It is necessary to know the mass of an object to find its potential energy.

We could also find this answer from the energy conservation law. At the start, the only type of energy is kinetic, `(mV_0^2)/2` and at the maximum height, the speed is zero and the only type of energy is potential, and they must coincide.