A ball thrown vertically upward reaches a maximum height of 30 m above the surface of the earth. What is the velocity of the ball at its maximum height, in meters per second?

Answer 1

This can be solved by conservation of energy.

As the ball flies higher, it is losing its initial initial kinetic, converting it to potential energy.

At the maximum height all of the initial kinetic energy has been converted to potential energy.

Let

v be the initial velocity (to be calculated),

m be the mass of the ball (unknown),

h = 30 m be the maximum height,

g = 9.81 m/s² be gravitational acceleration.

mv²/2 is the initial kinetic energy of the ball.

mgh is the potential energy of the ball at height h.

By convervation of energy

mv²/2 = mgh

From that calculate

v = √(2gh)

Substitute actual numbers

v = √(2×9.81×30) = 24.26 m/s