A-LevelPhysicsKinematics9702/23 · Oct/Nov 2021 · Q311 Marks

Define velocity.

(a)Define velocity.[1]
(b)A remote-controlled toy aircraft is flying horizontally in a wind. Fig. 3.1 shows the velocity vectors, to scale, of the wind and of the aircraft in still air. [Figure 3.1] The velocity of the aircraft in still air is 42ms⁻¹ to the north. The velocity of the wind is 23 ms⁻¹ in a direction of 54° east of south. Determine the magnitude of the resultant velocity of the aircraft.[2]
(c)The engine of the aircraft in (b) stops. The aircraft then glides towards the ground with a constant velocity at an angle θ to the horizontal, as illustrated in Fig. 3.2. [Figure 3.2] The aircraft has a weight of 46 N and travels a distance of 280 m from point X to point Y. The change in gravitational potential energy of the aircraft for its movement from X to Y is 6100 J. Assume that there is now no wind.
(c)(i)Calculate angle θ.[3]
(c)(ii)Calculate the magnitude of the force acting on the aircraft due to air resistance.[2]
(d)The aircraft in (c) travels from X to Y in a time of 14s. Fig. 3.3 shows that, as the aircraft travels from X to Y, it moves directly towards an observer who is standing on the ground. [Figure 3.3] The aircraft emits sound as it travels from X to Y. The observer hears sound of frequency 450 Hz. The speed of the sound in the air is 340ms⁻¹. Calculate the frequency of the sound that is emitted by the aircraft.[3]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

[B1] change in displacement / time (taken)
[C1] by calculation: v² = 42² + 23² – (2 × 42 × 23 × cos 54°) or v² = (42 – 23 cos 54°)² + (23 sin 54°)² or v² = (42 – 23 sin 36°)² + (23 cos 36°)²
[A1] v = 34 m s⁻¹
or
[(C1)] by scale diagram: triangle of vector velocities drawn
[(A1)] v = 34 m s⁻¹ (allow ± 1 ms⁻¹ if scale diagram used)
[C1] (Δ)E = mg(Δ)h or (∆)E = W(Δ)h
[C1] h = 6100/46 (= 133 m)
[A1] θ = sin⁻¹ (133/280) = 28°
[C1] force = 6100/280 or 46 sin 28°
[A1] = 22 N
[C1] V(s) = 280 / 14 (= 20 ms⁻¹)
[C1] f₀ = f_s v/ (v - v_s)
[A1] f_s = 450 × (340 – 20) / 340 = 420 Hz

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