5. A child is playing with a small model of a fire-engine of mass 0.5 kg and a straight, rigid plank. The plank is inclined at an angle \(\alpha\) to the horizontal. The fire-engine is projected up the plank along a line of greatest slope. The non-gravitational resistance to the motion of the fire-engine is constant and has magnitude \(R\) newtons. When \(\alpha = 20 ^ { \circ }\) the fire-engine is projected with an initial speed of \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and first comes to rest after travelling 2 m .

1. Find, to 3 significant figures, the value of \(R\). When \(\alpha = 40 ^ { \circ }\) the fire-engine is again projected with an initial speed of \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
2. Find how far the fire-engine travels before first coming to rest.