3 The maximum power produced by the engine of a small aeroplane of mass 2 tonnes is 128 kW . Air resistance opposes the motion directly and the lift force is perpendicular to the direction of motion. The magnitude of the air resistance is proportional to the square of the speed and the maximum steady speed in level flight is \(80 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).

1. Calculate the magnitude of the air resistance when the speed is \(60 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The aeroplane is climbing at a constant angle of \(2 ^ { \circ }\) to the horizontal.
2. Find the maximum acceleration at an instant when the speed of the aeroplane is \(60 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).