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A cyclist travels a distance of $4 km$ from $a$ to $b$ and then moves a distance of $3 km$ at right angle to $ab$ . Find his displacement?

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6 km

5 km

4 km

3 km

answer is B.

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Detailed Solution

A cyclist travels a distance of

4 km

from

a

b

and then moves a distance of

3 km

at right angle to

ab

. The displacement of the cyclist is

5 km

.
According to the information provided, the biker covered

4 km

before covering

3 km

. When represented graphically, these are perpendicular to one another and create a triangle.
Question Image

The given vectors are

b

and

a

, where

b = 4

and

a = 3

. Thereby, we have resultant displacement,

c^{2} = b^{2} + a^{2}

R = \sqrt{4^{2} + 3^{2}}

= \sqrt{16 + 9}

= \sqrt{25}

= 5 km

, since displacement can never be negative.

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