Define velocity in terms of displacement and time.
A remote-controlled toy aircraft is flying horizontally in a wind. Fig. 3.1 gives, to scale, the velocity vectors for the wind and for the aircraft in still air. The aircraft’s velocity in still air is $42\,\text{m s}^{-1}$ north. The wind’s velocity is $23\,\text{m s}^{-1}$ at $54^\circ$ east of south. Determine the magnitude of the aircraft’s resultant velocity.
The engine of the aircraft in (b) fails. It then glides to the ground at constant velocity, making an angle $\theta$ with the horizontal, as shown in Fig. 3.2. The aircraft weighs $46\ \text{N}$ and covers a distance of $280\ \text{m}$ from point X to point Y. During its motion from X to Y, the change in gravitational potential energy of the aircraft is $6100\ \text{J}$. Assume that the wind is now absent. Calculate angle $\theta$.
Calculate the magnitude of the force on the aircraft due to air resistance.
The aircraft in (c) travels from X to Y in a time of $14\ \text{s}$. Fig. 3.3 shows that, as the aircraft moves from X to Y, it goes directly towards an observer standing on the ground. The aircraft emits sound while travelling from X to Y. The observer hears sound of frequency $450\ \text{Hz}$. The speed of sound in air is $340\ \text{m s}^{-1}$. Calculate the frequency of the sound emitted by the aircraft.