You are going to build a car that is propelled as far as possible on a path using a mousetrap as its source of energy.

How would I calculate the speed or distance of a mousetrap car? What are the steps 

Calculate the thermal energy dissipated from brakes in a 1260-kg car that descends a 14.5° hill. The car begins braking when its speed is 98 km/h and slows down to a speed of 30 km/h in a distance of 0.47 km measured along the road.

A cat is chasing a mouse. The mouse runs in a straight line at the speed of 1.0 m/s. If the cat leaps off the floor at 60* angle and a speed of 6.0 m/s, at what distance behind the mouse should the cat leap in order to land on the the mouse?

Calculate the force exerted on a rocket, given that the propellinggases are expelled at a rate of 1380 kg/s with a speed of 4.5 104m/s (at the moment of takeoff).

Answer in Newtons.

Please include formulas when possible.