Interesting Collision Problem (hard STEP level?)

Is that 160...(kg?) or m?

The only thing that matters is the ratio between the mass of the small truck and the mass of the large one. I am using m and M to denote these two masses.

To be honest, this is probably (definitely!) too hard for STEP as written. If people are interested I may post some hints.

A large truck of mass M is travelling towards a wall at constant speed.
A small truck of mass m is in the way.

All collisions (between the two trucks, and between the small truck and the wall) are perfectly elastic.

If M = 160000000000m, how many collisions occur between the trucks before the large truck starts moving away from the wall?

Why does the distance to the wall not matter?

The velocities only change when either the trucks collide or the small truck collides with the wall. The only way the distance would matter is if we cared how long it took between collisions, but we don't.

It's a bit messy, yes.

Some hints:

I formed a second order recurrence relation for the speed of object M alone.

It is of the form Mi+2=((Mi+1)^2 + A(Mi)(Mi+1))/Mi but it was just horrendous, in hindsight using vn and Vn makes a lot more sense.
But tbh I highly doubt I would have got any further anyway, after looking at the solution.

Oh well. Back to STEP lol.

For what it's worth, I've seen a variant of this on a CCE paper (the Cambridge Entrance Exam before STEP). But I think it was a 504 paper, where 3 complete questions would give you the equivalent of an S.

Does the 314159 come from the truck with mass m making a turn of 314159 radians every time it hits the wall and the truck with mass M? Is it a good idea to find out the number of turns the small truck makes and then halve that amount to get the answer.

No. The truck's are all moving in a straight line. (Each collision is just a standard M1/M2 collisions problem, it's just there are rather a *lot* of collision).

Do they collide 8 x 10^11 times?

To be honest, this is probably (definitely!) too hard for STEP as written. If people are interested I may post some hints.

A large truck of mass M is travelling towards a wall at constant speed.
A small truck of mass m is in the way.

All collisions (between the two trucks, and between the small truck and the wall) are perfectly elastic.

If M = 160000000000m, how many collisions occur between the trucks before the large truck starts moving away from the wall?

No.

I give up, just hope something similar doesn't come it this year

I give up, just hope something similar doesn't come it this year