# Two questions regarding linear momentum and conservation

Two questions regarding linear momentum and conservation....

## Homework Statement

See : http://postimg.org/image/e7vvycs5t/ [Broken]

Questions : 63 and 64

Sorry, the image is little blurred. I was in so hurry that I could not take a better snap shot. Please do not left click on the image. (You know to what extent the blurring can enhance.)

## Homework Equations

Conservation of law of conservation of linear momentum, and collision equations.

## The Attempt at a Solution

For first :

For body 1 : v1 = 0

For body 2 :

v2 = u1

"v[index]" is final velocity of body 1 or 2.
u1 is initial velocity of body 1.

Ok, so how does this imply that bodies go right angle at each other ?

For second :

I seriously do not know how to begin. I am sorry. Is there some sort of geometry ? I cannot follow the hint given in the book.

Please hep !!

Thanks in advance... Last edited by a moderator:

## Answers and Replies

For problem 63, apply the equations for conservation of kinetic energy and conservation of momentum along the x and y axes. By a few steps of mathematical juggling you should be able to get cos(α+β)=0 {where α and β are the angles made by the final velocity vectors with the initial direction of motion).
Problem 64 is an extension of 63

P.S. assume the X axis to be along the initial velocity.

Last edited:
For problem 63, apply the equations for conservation of kinetic energy and conservation of momentum along the x and y axes. By a few steps of mathematical juggling you should be able to get cos(α+β)=0 {where α and β are the angles made by the final velocity vectors with the initial direction of motion).
Problem 64 is an extension of 63

P.S. assume the X axis to be along the initial velocity.

Alright. Ok, I did a mistake while reading the question ! It was not a "Head On" collision, though elastic.

Applying conservation of linear momentum :

v1 + v2 = u1

Note that mass cancels and symbols denote the general meaning as I stated in the previous post. Writing in magnitude form :

v12+v22+2v1v2cos(θ) = u12 ...(i)

Applying conservation of kinetic energy :

Note that factor m/2 cancels and,

v12+v22=u12 ...(ii)

Subtracting (ii) from (i) , we get :

v1v2cosθ=0. This implies θ=90o

θ is angle between two final velocity vectors.

I could have also done this by component method.

Thanks a bunch Sunil !!

Now to next question :

Can I get more hints ?

Also, are you preparing for IIT ? Did you recognize the book from which I asked this question ? :)

Yes I'm preparing for the JEE too. Good to see a fellow student. No, I did not recognize the book (I'm guessing Irodov). As for the next question, now that you are armed with the result of the Q63, I guess you should be able to solve it.

Yes I'm preparing for the JEE too. Good to see a fellow student. No, I did not recognize the book (I'm guessing Irodov). As for the next question, now that you are armed with the result of the Q63, I guess you should be able to solve it.

Yep solved it !! Thanks again. And it was from H.C. Verma. BTW, I have just passed 11th.

And regarding your PM:

My internet was unable to load the image of that thread, which "Beast" posted. When I try to open it in a separate tab, it gives a server error.