# The body is thrown vertically upward with a speed v, find the height of the body

The path for uniformly accelerated motion is determined by the formula:

S = v start * t + (аt²) / 2, where S – path, distance, v start – initial speed, t – time, and – acceleration.

In our case, the movement of the body is carried out upward with a speed of v beginning, and it occurs equally slowly – its speed falls all the time, because gravity acts against it, which slows down its movement with the acceleration of gravity – v down = g * t (where g – acceleration of gravity).

As long as the speed (v up) of the upward movement exceeds the downward speed, the body moves upward, slowing down all the time. Finally, when the velocities equal (v up = v down), the body stops moving up, “stops” at the maximum height of its rise, in order to start free fall with a known acceleration down.

Then the equation will take the form: S up = v start * t – (gt²) / 2.

The maximum height to which the body can rise is determined by the formula – h max = v² start / 2g.