Help with a few exam questions?

Hi, I'm struggling with the following 3 questions and would appreciate some help - thanks. I know what the answers are but don't know why they're right.

1. Two electrical heating coils, L and M, are made from wires of the same material. The wires are of equal length but different diameters. L runs at twice the voltage of M but both coils dissipate the same power. What is the correct conductance ratio for the two coils L/M. (answer is 1/4)

2. A ball rolls up a ramp which is at angle 20 degrees to the horizontal. The speed of the ball at the bottom of the ramp is 2.2m/s. L is the distance the ball moves along the ramp before coming to rest. What is the distance L? Ignore the effects of friction and rotation. (answer is 0.72m)

3. A firework rocket with a mass of 0.4kg is launched vertically upwards with an inital acceleration of 6.2m/s/s. What is the force on the rocket from the burning fuel. (the answer is 6.4N, I see that comes from (9.8+6.2) x 0.4, but I don't understand why we're taking gravity into account, and if we are, why we aren't using -9.8)

Thanks!

1. consider P=V²/R ... and we know the ratio of voltages is 2/1

2. did you try conservation of energy? (initial KE = maximum GPE gained)

3. 9.8 x 0.4 is the amount of thrust required to support the rockets weight against gravity - if this was all the thrust the rocket would be able to hover above the earths surface.
6.2 x 0.4 is the amount of thrust required to accelerate the rocket at 6.2 m/s² after overcoming gravity

another way of looking at it would be thrust to weight ratio (TWR)
TWR <1 means rocket stays on the pad
TWR >= 1 means rocket accelerates upward at (TWR-1) in units of g

Thanks a lot! I now totally understand 1 and 3, still struggling a little with 2. Using 1/2mv^2 = mgh, I rearranged to get the height of the incline as v^2/2g, = 0.247m but I'm not sure how to then use that to calculate the length of the slope or whether I was right to use v = 2.2, instead of 2.2sin20 or 2.2cos20.