A truck of mass 900 kg is towing a trailer of mass 150 kg up an inclined straight road with constant speed \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The trailer is attached to the truck by a light inextensible towbar which is parallel to the road. The road is inclined at an angle \(\theta\) to the horizontal, where \(\sin \theta = \frac { 1 } { 9 }\). The resistance to motion of the truck from non-gravitational forces has constant magnitude 200 N and the resistance to motion of the trailer from non-gravitational forces has constant magnitude 50 N .
Find the rate at which the engine of the truck is working.
When the truck and trailer are moving up the road at \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) the towbar breaks, and the trailer is no longer attached to the truck. The rate at which the engine of the truck is working is unchanged. The resistance to motion of the truck from non-gravitational forces and the resistance to motion of the trailer from non-gravitational forces are still forces of constant magnitudes 200 N and 50 N respectively.
Find the acceleration of the truck at the instant after the towbar breaks.
Use the work-energy principle to find out how much further up the road the trailer travels before coming to instantaneous rest.