Calculating Momentum and Speed: IGCSE Forces and Motion Textbook Example

[SuchBants]

Homework Statement

V of Alpha at T1 = 10^7
V of Alpha at T2 = 0.6 x 10^7
Mass of Alpha = 4x mass of proton

Homework Equations

P=MV
P1 = P2

The Attempt at a Solution

Bear in mind that I am a year 11 IGCSE student. This is from the textbook at the end of the chapter of forces and motion detailing simple momentum and speed equations.
I've tried many solutions that produce varied results for me.

 

[DrClaude]

Can you show us what you have obtained and explain why you think it is incorrect?

 

[SuchBants]

I could only ever get as far as arranging the equation using the principle that Momentum before = momentum after. But as I have no values for the masses I found I could not rearrange.
p₁= 4m x 10⁷
P₂= (4m x10⁷x0.6) + (m x V)
P₁ = P₂

As you can see I'm stumped here.

 

[DrClaude]

I could only ever get as far as arranging the equation using the principle that Momentum before = momentum after. But as I have no values for the masses I found I could not rearrange.
p₁= 4m x 10⁷
P₂= (4m x10⁷x0.6) + (m x V)
P₁ = P₂

As you can see I'm stumped here.

You just need to continue. In that last equation, substitute P₁ and P₂ using the other equalities you have, and try and find and equation for V.

 

[SuchBants]

But surely it would be impossible to get a value for V ? Given that we don't know the mass of m or 4m.

 

[DrClaude]

But surely it would be impossible to get a value for V ? Given that we don't know the mass of m or 4m.

Write out the equations and see what happens.

 

[SuchBants]

Sorry for the late reply.

I reached an answer and my working is attached.
Is it okay to presume M as any number? As long as the ratio of the mass stays 4:1?