Projectiles

Apr 2012
180
0
Srilanka
Hi,
I have a weird problem in projectiles, Anyone who can answer this problem?

The two balls P and Q are projected from a horizontal point O. A bird (a) distance from O was hit by ball P. Then the bird goes vertically into the sky with the velocity of U.When the bird return to the ground it hits by the second ball Q.So prove \(\displaystyle V^2=U^2+ag\)
 

chiro

MHF Helper
Sep 2012
6,608
1,263
Australia
Hey srirahulan.

Can you show us what you have tried? Any partial attempts and ideas you have had well help immensely.
 

topsquark

Forum Staff
Jan 2006
11,602
3,458
Wellsville, NY
Hi,
I have a weird problem in projectiles, Anyone who can answer this problem?

The two balls P and Q are projected from a horizontal point O. A bird (a) distance from O was hit by ball P. Then the bird goes vertically into the sky with the velocity of U.When the bird return to the ground it hits by the second ball Q.So prove \(\displaystyle V^2=U^2+ag\)
It can't be done with only this information. First of all we need a relationship between the mass of the ball and the mass of the bird. Second if the bird is on the ground before ball P hits it and the bird is propelled upward at speed U ball V is going to be pressed into the ground in a perfectly inelastic collision. We don't know how much energy ball P has after the collision. Finally when ball Q hits the bird as it is on its way down, the bird will presumably shoot back up into the air. It can't be going up at a speed U because it was moving downward at a speed U at the time of the collision. Is the bird now stationary?

We can get around some of this. At the collision of ball P hitting the bird we can go ahead (for the sake of argument) and assume that all the momentum of ball P went into the bird going upward at U. (Never mind that this is a gross violation of conservation of momentum.) We can make a prediction based on this: when ball Q hits the bird, the bird (somehow) and ball Q end up with a speed of 0.

Even with these (absurd) assumptions we still need the mass of the bird and the mass of the ball.

If there is another sequence for this chain of events, please let us know.

-Dan