Question

A cannon directed straight upward launches a ball with an initial speed v. The ball reaches a maximum height h in a time t. Then, the same cannon is used to launch a second ball straight upward at a speed 2v. In terms of h and t, what is the maximum height the second ball reaches and how long does it take to reach that height? Ignore any effects of air resistance.

Answer 1

The first ball is launched with an initial speed v.

At the topmost point, the ball will come to rest.

Using the kinematics equation,

where f and i denotes the final and initial velocity and f is the acceleration and t is the time required.

Here the ball is launched vertically upwards, so the acceleration on the ball is the acceleration due to gravity acting downwards.

Hence, we can write

It reaches the maximum height of h in time t,

So, we can write

Now, another ball is released with velocity 2v.

Let it will reach a maximum height of h' in time t'

Using equation (i)

Now,

Using equation (ii)

So, maximum height reached by the new ball in terms if h is

And time required to reach h' is