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Vector Addition

Car A and Car...

Question

Car A and Car B starts from origin with speeds $54$ kmph and $72$ kmph respectively. Both starts from origin at the same time. Find the distance between A and B after $20$ minutes .

A

54

km

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B

30

km

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C

24

km

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D

47

km

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Solution

The correct option is B $30$ km
Given $t = 20 m i n = \frac{1}{3} h r$

$X_{A} = v_{1} t = 54 \times \frac{1}{3} = 18 k m$
$Y_{B} = v_{2} t = 72 \times \frac{1}{3} = 24 k m$
Distance between A and B is
$d = \sqrt{X_{A}^{2} + Y_{B}^{2}} = \sqrt{18^{2} + 24^{2}} = 6 \sqrt{3^{2} + 4^{2}} = 30 k m$

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