Aball is thrown straight up with an initial speed of 16.9 m/s. at what height above its initial position will the ball have one‑half its initial speed?

10.9 m

Explanation:

We can solve the problem by using the law of conservation of energy.

The initial mechanical energy is just the kinetic energy of the ball:

where m is the mass of the ball and u = 16.9 m/s the initial speed.

At a height of h, the total mechanical energy is sum of kinetic energy and gravitational potential energy:

where v is the new speed, g is the gravitational acceleration, h is the height of the ball.

Due to the conservation of energy,

(1)

Here, at a height of h we want the speed to be 1/2 of the initial speed, so

So (1) becomes

So we can find h:

wavelength divides in half and speed stays the same.