Two questions regarding linear momentum and conservation

[sankalpmittal]

Two questions regarding linear momentum and conservation...

Homework Statement

See : http://postimg.org/image/e7vvycs5t/

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...

 

[Sunil Simha]

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.

 

[sankalpmittal]

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=90^o

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 ? :)

 

[Sunil Simha]

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.

 

[sankalpmittal]

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.