Question 10
Two canoes M and N started from a shore A at the same time. M sails at 35 km/h on a bearing of 230 while N sails at 30 km/h on a bearing of 320. If the two canoes sailed for 2.5 hours, find, correct to one decimal place, the:
- distance between M and N;
- bearing of M and N.
Observation
The Chief Examiner reported that the performance of candidates who attempted this question was encouraging because many were able to solve it correctly.
In part(a), they were expected to the distances as Distance travelled by M = 35 2.5 = 87.5km and Distance travelled by N = 30 2.5 = 75km.
In part (b), they were expected to draw the diagram as shown:
Using Pythagoras theorem and substituting gives |MN|2 = 752 + (87.5)2. Solving gives |MN| = = 115.244 = 115.2km. Let = MNA then tan = . = tan-1 = 49.4o.
Bearing of M from N = 90 + 50 + 49.4 = 189.4o = 189o.