Crazy Projectiles
A particle of mass is projected vertically upwards with velocity . In its return journey it collides with another particle of mass , below the maximum height attained by particle . Particle has a horizontal velocity and vertical velocity . Find the distance between the places they hit the ground.
Details and assumptions
- The collision has a coefficient of restitution
- Acceleration due to gravity
The answer is 200.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
We see that this is inelastic collision so here the conservation of kinetic energy is not applicable as some amount of energy is lost to the surroundings. Now here conservation of momentum is always applicable along the line of impact which is the line joining the centers of the balls during collision. However the velocity of the bodies along the line perpendicular the the line of impact is same. Make equations for both bodies as instructed above. Let's call the vertically moving ball as ball 1 and the other as ball 2. After solving the equations above you will find that Velocity of ball 1 is -100 i+ 0j And velocity of ball 2 is -200i - 80j Now using kinematics we can find the range of both the bodies For ball one we get range as 600m. And for ball 2 we get range is 400m. Thus difference is 200. Which is the answer.