Question

Consider a ball being fired straight up (purely in the y-direction). If the ball has a maximum height of H above the launcher, you should be able to calculate the initial velocity of the ball, v₀ , as it leaves the launcher. Answering the questions below will help you accomplish this task.

First draw a diagram of the situation. Clearly label H , v₀ , and the point you select as your origin.

What will the velocity of the ball be when it achieves its maximum height?

Use 1-D kinematics to determine the initial launch velocity, v₀ , required for the ball to attain this height. Give your answer in terms of H and g.

Answer 1

In motion under gravity if a ball is thrown up then at topmost point it's velocity will be zero.
Because to return back to ground it has to stop somewhere which is its topmost point.

The motion here is motion under gravity and acceleration in this case is constant , which is equal to gravitational acceleration which is in downward direction and constant.
so, we can apply here the formula of kinematics:


and for motion under gravity it will be as follows:
where, v = final velocity , u= initial velocity , g = gravitational acceleration
   and h= height or displacement.
In the above problem,
v = 0, since it will be at maximum height for displacement = H,
now put the value in equation,

where = initial velocity or velocity with which tha ball is launched from ground.

hence is the required answer.