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**1. The problem statement, all variables and given/known data**

I am a GCSE Physics student, and my teacher recently set us a homework sheet in which he said contained questions 'exceeding A-Level standard'. He told us to get as far as we could. So, I have completed 12 of 18 questions, but I am very confused about the last 6:

1) A 3kg trolley moving at 40cm/s collides with and joins to a stationary trolley of mass 2kg on a horizontal, frictionless surface. Calculate the speed at which the trolleys move after the collision and the loss of kinetic energy.

2) Two trolleys, each of mass 2kg, collide and stick together on a smooth, horizontal surface. One trolley is at rest before the collision. The other moves at 20cm/s before the collision. Calculate the combined velocity (size and direction) of the trolleys after the collision.

3) Two trolleys, both of mass 2kg, are moving in the same direction along a smooth surface. One is moving faster (30cm/s) and catches up the other (20cm/s). The trolleys collide and stick together. Calculate the combined velocity (size and direction) of the trolleys after the collision.

4) Two trolleys (one of mass 2kg, travelling at 30cm/s and one of mass 3kg, travelling at 20cm/s) are moving in opposite directions along a smooth surface. The trolleys collide and stick together.

a) What is the total momentum of the trolleys before and after the collision?

b) What is the trolleys' combined velocity after the collision?

5) A car of mass 1500kg, travelling at 15m/s, collides 'head on' with a second car, mass 1000kg, which has a speed of 16.5m/s in the opposite direction. Find the speed and direction of the cars immediately after the collision, assuming that they remain locked together.

6) Two trolleys, of mass 2kg and 5kg, are at rest and in contact on a smooth, level surface. A coiled spring in one trolley is released so that they 'explode' apart. The lighter trolley moves off at 50cm/s. Find the speed of the heavier trolley and the minimum energy which was stored in the coiled spring before release.

**2. Relevant equations**

I am unsure of the necessary equations to complete these questions, and would appreciate anyone who could tell me them, what they mean and how I can apply them to work out the answers.

**3. The attempt at a solution**

I have tried for 3 days to find a solution to these questions, searching for formulas and asking past A-Level Physics students, but I am really struggling to understand how to work the answers out.

Many thanks,

tomclaessens