3 A lorry has mass 12000 kg .
- The lorry moves at a constant speed of \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) up a hill inclined at an angle of \(\theta\) to the horizontal, where \(\sin \theta = 0.08\). At this speed, the magnitude of the resistance to motion on the lorry is 1500 N . Show that the power of the lorry's engine is 55.5 kW .
When the speed of the lorry is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) the magnitude of the resistance to motion is \(k v ^ { 2 } \mathrm {~N}\), where \(k\) is a constant. - Show that \(k = 60\).
- The lorry now moves at a constant speed on a straight level road. Given that its engine is still working at 55.5 kW , find the lorry's speed.