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PHYSICS, M1 EQ-Bank 18

A helicopter is cruising with an airspeed, \(v_1\), of 220 km/h. The pilot wishes for its flight path to be due south. However, a crosswind, \(v_2\), of 60 km/h is blowing from the west.

Using a vector diagram, in which direction should the pilot steer the helicopter to achieve a due south course?   (3 marks)

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\(\text{S}16^{\circ}\text{W}\)

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\(\sin \theta\) \(=\dfrac{v_2}{v_1}\)  
\(\theta\) \(=\sin^{-1}\left(\dfrac{60}{220}\right)=16^{\circ}\)  

 
\(\therefore\) The pilot must steer the helicopter \(\text{S}16^{\circ}\text{W}\).

PHYSICS, M1 EQ-Bank 7

Below is a description of the motion of a runner. The motion can be divided into three stages.

Stage 1: Runner travels 120 metres south taking 20 seconds.

Stage 2: Runner turns west and travels at 5 ms\(^{-1}\) for half a minute.

Stage 3: Runner travels directly back to their starting position.

  1. Determine the distance that the runner ran during Stage 2 of their journey.   (1 mark)
  2. Find the displacement of the start point from the runner Stage 2 is completed.   (3 marks)

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a.    \(\text{150 m}\)

b.    \(\text{192.1 m, N51.3°E.}\)

Show Worked Solution

a.   \(d=v \times t=5 \times 30=150\ \text{m}\)
 

b.    Stage 1 and Stage 2 displacement diagram:
 

Using Pythagoras:

\(d=\sqrt{150^2 + 120^2}=\sqrt{36900}=192.1\ \text{m}\)
 

\(\tan\,\theta\) \(=\dfrac{120}{150} \)  
\(\theta\) \(=\tan^{-1}\Big(\dfrac{120}{150}\Big)=38.7^{\circ}\)  

 
\(\therefore\) Displacement of the start point from the runner is 192.1 m, N51.3°E.