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