This diagram is a scale drawing used by a coastguard team. A rescue boat travels 3.0 km due east from a harbour, then 4.0 km due north to a buoy. The team d...
Question 1 Report
This diagram is a scale drawing used by a coastguard team. A rescue boat travels 3.0 km due east from a harbour, then 4.0 km due north to a buoy. The team distinguishes between the distance moved by the boat and its displacement from the harbour. Sea waves make the actual route slightly curved, but the drawing is used as an approximation.
(a) State the total distance travelled using the two straight sections shown. [1]
(b) Calculate the magnitude of the boat's displacement from the harbour. [2]
(c) Describe the direction of this displacement. [3]
(d) Explain why the boat's average speed can be found without knowing its final direction, but its average velocity cannot. [4]
Answer Details
(a) \[\text{total distance}=3.0+4.0=7.0\text{ km}\]
The total distance is 7.0 km. [1]
(b) The east and north movements form a right-angled triangle:
\[\text{displacement}=\sqrt{3.0^2+4.0^2}=\sqrt{25}=5.0\text{ km}\]
The displacement magnitude is 5.0 km. [2]
(c) The displacement direction is north-east. [1] Its angle must be stated from a named direction. [1] For example, it is \(53^\circ\) north of east, or equivalently \(37^\circ\) east of north. [1]
(d) Average speed uses total distance travelled [1] divided by total time. [1] Speed has no direction. [1] Average velocity uses displacement, which has a direction, so the final direction is needed. [1]
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