Question

a projectile is projected with a linear momentum P making angle e with the horizontal . the change in momentum of the projectile on return to the ground state will be:

a.2p
b. 2p cos theta
c.2p sin theta
d. 2p tan theta

Answer 1

Given:

A projectile is projected with a linear momentum P making angle $\theta$.

To find:

Change in momentum of Projectile upon reaching the ground.

Concept:

Any projectile motion can be imagined as 2 simultaneously occuring linear motions occuring in x and y axis.

Similarly the linear momentum of the projectile can be divided into vector components along x and y axis.

Now , upon completing the trajectory , the x axis component of momentum doesn't change due to absence of acceleration along x axis.

But , along the y axis , the linear Momentum becomes equal and opposite in direction after reaching the ground.

Calculation:

Linear momentum change along x axis :

$\therefore \: \Delta P_{x} = P \cos( \theta) - P \cos( \theta)$

$= > \Delta P_{x} =0$

Linear Momentum change along y axis :

$\therefore \: \Delta P_{y} = P \sin( \theta) - \bigg \{ - P \sin( \theta) \bigg \}$

$= > \Delta P_{y} = 2P \sin( \theta)$

So net change in momentum will be :

$\boxed{ \bold{ \Delta P_{net} = 2P \sin( \theta) }}$