1. \hspace{0pt} [In this question use \(\mathrm { g } = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) ]

A jogger of mass 60 kg runs along a straight horizontal road at a constant speed of \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The total resistance to the motion of the jogger is modelled as a constant force of magnitude 30 N .

1. Find the rate at which the jogger is working. The jogger now comes to a hill which is inclined to the horizontal at an angle \(\alpha\), where \(\sin \alpha = \frac { 1 } { 15 }\). Because of the hill, the jogger reduces her speed to \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and maintains this constant speed as she runs up the hill. The total resistance to the motion of the jogger from non-gravitational forces continues to be modelled as a constant force of magnitude 30 N .
2. Find the rate at which she has to work in order to run up the hill at \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).