Cambridge International Mathematics

Example 4 Self Tutor

Sonya can swim at 3 km/h in calm water. She swims in a river where the current is 1 km/h in an

easterly direction. Find Sonya’s resultant velocity if she swims:

a with the current b against the current c northwards, across the river.

Scale: 1 cm ́ 1 km/h

The velocity vector of the river is

a Sonya’s velocity vector is

The net result is r+s.

) Sonya swims at 4 km/h in the direction of the current.

b Sonya’s velocity vector is

The net result is r+s.

) Sonya swims at 2 km/h against the current.

c

Sonya’s velocity vector is and the net result is r+s.

) jr+sj=

p

10 ¼ 3 : 16

tanμ=^13 so μ= tan¡^1 (^13 )¼ 18 : 4 o

) Sonya swims at about 3 : 16 km/h in the direction 018 : 4 o:

EXERCISE 24C

1 Copy the given vectorspandqand hence show how to find p+q:

ab

cd

r

rs

s

rs¡¡+

r

s

s

rs¡¡+

r

s

N rs¡¡+

q

q

~` 1 ` 0 3

1

q

s

N

S

WE

p

q

p

q

p q

q

p

488 Vectors (Chapter 24)

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Y:\HAESE\IGCSE01\IG01_24\488IGCSE01_24.CDR Monday, 27 October 2008 2:26:43 PM PETER