Question

A projectile of mass 100 kg is lunched from a tower 100 m above the ground in horizontal direction with initial velocity 100m/s. At some time, explosion splits the projectile in two pieces. One piece, of mass 60 kg is observed to hit the ground 400 m away from the tower after 4 s. Find the location of the second fragment at the same time.

Not sure how to approach it, I tried using conservation of momentum but that didn't work would I need to do center of mass?

Answer 1

Assume that the collision seperated the fragments horizontally, and that the fragment did not acquire any vertical velocity due to explosion.

The projectile will hits the ground travelling a vertical distance (if there is no explsion) after a time .

Using

( since velocity in the vertical direction is zero , )

The horizontal distance travelled by the projectile (if there is no explosion) is

( since )

That is the location of center of mass of the two fragments is at

If the position of fragment with mass is and position of fragment with mass is

Location of second fragment is