A small remote-controlled model aircraft has two propellers, each of diameter 16cm. Fig. 3.1 is a side view of the aircraft when hovering. [Figure 3.1] Air is propelled vertically downwards by each propeller so that the aircraft hovers at a fixed position. The density of the air is 1.2kgm⁻³. Assume that the air from each propeller moves with a constant speed of 7.6ms⁻¹ in a uniform cylinder of diameter 16cm. Also assume that the air above each propeller is stationary.

1. (a)Show that, in a time interval of 3.0s, the mass of air propelled downwards by one propeller is 0.55 kg. [3][3]
2. (b)(i)Calculate: the increase in momentum of the mass of air in (a) increase in momentum = ............................................. Ns [1][1]
3. (b)(ii)the downward force exerted on this mass of air by the propeller. force = .................................................... N [1][1]
4. (c)(i)State: the upward force acting on one propeller force = .................................................... N [1][1]
5. (c)(ii)the name of the law that explains the relationship between the force in (b)(ii) and the force in (c)(i). [1][1]
6. (d)Determine the mass of the aircraft. mass = .................................................... kg [1][1]
7. (e)In order for the aircraft to hover at a very high altitude (height), the propellers must propel the air downwards with a greater speed than when the aircraft hovers at a low altitude. Suggest the reason for this. [1][1]
8. (f)When the aircraft is hovering at a high altitude, an electric fault causes the propellers to stop rotating. The aircraft falls vertically downwards. When the aircraft reaches a constant speed of 22 m s⁻¹, it emits sound of frequency 3.0 kHz from an alarm. The speed of the sound in the air is 340 ms⁻¹. Determine the frequency of the sound heard by a person standing vertically below the falling aircraft. frequency = .................................................... Hz [2][2]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.