Applications in Bearings and Navigation

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Applications in Bearings and Navigation — Free MYP5 Mathematics (Standard) Practice Questions

1QuestionUsing Scale and Bearings TogetherConcept Practice

4 marks~6 minCriterion A

A search-and-rescue team uses a map with a scale of

1:50\,000

. On the map, the straight-line distance between base camp

A

and a reported incident site

B

measures

8.4

cm. The bearing from

A

B

065°

Explain how the scale

1:50\,000

is used to convert the map distance to an actual ground distance. [1]

Determine the actual ground distance between

A

and

B

in kilometres. [2]

The rescue team can travel at most

5

km before requiring a resupply. Advise the team leader whether the team can depart from base camp

A

and reach site

B

without a resupply, justifying your advice with a numerical comparison. [1]

Solutions

2QuestionDrawing Diagrams from Bearings DescriptionsAssessment Practice

6 marks~9 minCriterion D

A ship departs from port A and sails on a bearing of

060°

for 12 km to reach point B. It then changes course to a bearing of

150°

and travels 8 km to arrive at point C. A coastguard vessel at port A can only respond to emergencies within a 7 km radius.

Construct a diagram of the ship's journey. Include north lines at A, B, and C, and label all points and distances. [2]

Deduce the angle

\angle ABC

. [2]

The ship reports an emergency at point C. Advise the coastguard commander at A whether the vessel should be dispatched, justifying your answer with a calculated distance. [2]

Solutions

3QuestionUsing Scale and Bearings TogetherConcept Practice

2 marks~3 minCriterion B

A coastguard station records four rescue vessels departing on different bearings.

Bearing	$030°$	$060°$	$120°$	$150°$
Clockwise angle from north	$30°$	$60°$	$120°$	$150°$

Describe the relationship between a bearing and its clockwise angle from north. [1]

A fifth vessel departs on a clockwise angle of

80°

from north. A safe shipping lane begins at a bearing of

080°

. Justify whether this vessel is travelling along the safe shipping lane, using bearing notation in your answer. [1]

Solutions

4QuestionDrawing Diagrams from Bearings DescriptionsAssessment Practice

8 marks~12 minCriterion C

A surveyor maps a closed path using four legs. The first three legs are:

Leg 1	bearing 030°	distance 5 km
Leg 2	bearing 150°	distance 5 km
Leg 3	bearing 270°	distance 5 km

Analyse the pattern in the bearings of Legs 1, 2, and 3, and deduce the bearing of Leg 4 that would continue this pattern to close the path. [2]

Calculate the resultant displacement after completing Legs 1, 2, and 3 by resolving each leg into its north and east components. [3]

Advise the surveyor whether Leg 4 should be included in the route plan, justifying your recommendation using your result from part (b) and the geometry of the path. [3]

Solutions

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