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Question

Car A has an acceleration of 2 m/s2 due east and car B, 4 m/s2 due North. Acceleration of car B with respect to car A is

A
25 at an angle tan1(2) North of West.
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B
25 at an angle tan1(2) West of North.
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C
42 at an angle tan1(13) North of West.
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D
42 at an angle tan1(13) West of North.
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Solution

The correct option is A 25 at an angle tan1(2) North of West.
This is a two - dimensional motion.

Let North and East directions by positive y axis and x axis respectively.
Therefore, aBA= acceleration of car B with respect to car A
=aBaA
Here, aB= acceleration of car B =4^j m/s2
And aA= acceleration of car A =2^i m/s2
aBA=(4^j2^i) m/s2

aBA=(4)2+(2)2=25 m/s2
And a=tan1(42)=tan1(2)

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