A roller coaster car is at rest at point as shown.

Determine the height, , of the roller coaster at point if it is travelling at 30 m/s at that point. Assume no energy losses.   (3 marks)

The diagram shows a drop hammer being used to drive a pile into the ground.
 

Which formula gives the height required for the drop hammer to impact the pile at a pre-determined velocity ?

A bike with a rider rolls down a hill without braking from a standing start at point .
 

The combined weight of the bike and the rider is 100 kg.

Calculate the speed of the rider at point . (Assume no wind resistance and 100 % efficiency.)   (2 marks)

A scooter and rider enter the half pipe shown at a velocity of 3 m/s. The scooter and rider have a combined mass of 55 kg.
 

Calculate the maximum height, , the scooter and rider will reach above the other side of the pipe wall. Assume no loss of energy.   (3 marks)