Math Help - Projectiles Question

1. Projectiles Question

A particle of mass m is projected vertically upwards with speed u and when it reaches its greatest height a second particle of mass 2m is projected vertically upward with speed 2u from the same point as the first.

a) Prove that the time that elapses between the projection of the second particle and the collision with the first is u/4g

b) Find the height above the ground at which this occurs

If on collision the particles coalesce prove that the combined particle will reach a greatest height of 19U power 2 / 18g above the point of projection.

2. Originally Posted by Tilleard
A particle of mass m is projected vertically upwards with speed u and when it reaches its greatest height a second particle of mass 2m is projected vertically upward with speed 2u from the same point as the first.

a) Prove that the time that elapses between the projection of the second particle and the collision with the first is u/4g

b) Find the height above the ground at which this occurs

If on collision the particles coalesce prove that the combined particle will reach a greatest height of 19U power 2 / 18g above the point of projection.
Is it to be assumed that air resistance is negligible?

3. Originally Posted by Tilleard
A particle of mass m is projected vertically upwards with speed u and when it reaches its greatest height a second particle of mass 2m is projected vertically upward with speed 2u from the same point as the first.

a) Prove that the time that elapses between the projection of the second particle and the collision with the first is u/4g

b) Find the height above the ground at which this occurs

If on collision the particles coalesce prove that the combined particle will reach a greatest height of 19U power 2 / 18g above the point of projection.
First find the greatest height of the first particle.

Take the time of greatest height (call this height $h_{max}$) of the first particle as $0$. Now the problem (a) is that of finding the time of collision of an upward projected particle from $h=0$ with initial speed of $2u$ and one falling from rest from $h_{max}$

CB