Calculate the maximum height achieved by a ball thrown straight into the air with initial speed 20.0 ft/sec. Give the answer to 1 decimal place.

Question

Calculate the maximum height achieved by a ball thrown straight into the air with initial speed 20.0 ft/sec. Give the answer to 1 decimal place.

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 = 20.0 ft/sec be the initial speed,

m be the mass of the ball (unknown),

h be the maximum height (to be computed),

g = 32.1 ft/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 conservation of energy

mgh = mv²/2

From that calculate

h = v²/2g

Substitute actual numbers

h = 20.0²/(2×32.1) = 6.2 ft