A girl throws a tennis ball upward with an initial velocity of 4 m/s. What is the maximum displacement of the ball?
A tennis ball will go up and its velocity will decrease. When the velocity is zero, the ball will be at its maximum height and will begin to fall down. This maximum height is what we are solving for.
The easiest way to find this is to consider energy. Energy will be conserved, so the energy of the ball at the start and at the point of maximum height will be the same.
At the start a ball has only kinetic energy `(mV^2)/2,` where `m` is the mass and `V` is the initial speed. In contrast, at the maximum height it will have only the potential energy `mgh` where `h` is the maximum height.
So `(mV^2)/2=mgh,` i.e. `V^2/2=gh` and `h=V^2/(2g) approx 16/20` = 0.8 (m). This is the answer.
Note that we ignored air resistance. If we hadn't, the real height would be less.
For future reference, the formula below can be used to solve similar problems.
The formula is `h=(V^2)/(2g)` where `h` is the maximum height (maximum displacement) and `V` is the initial upward velocity.