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Particle A moves along X-axis with a uni...

Particle A moves along X-axis with a uniform velocity of magnitude 10 m/s. Particle B moves with uniform velocity 20 m/s along a direction making an angle of 60° with the positive direction of X-axis as shown in the figure. The relative velocity of B with respect to that A is

A

10 m/s along X-axis

B

`10sqrt(3)` m/s along Y-axis (perpendicular to X-axis)

C

`10sqrt(5)` m/s along the bisection of the velocities of A and B.

D

30 m/s along negative X -axis.

Text Solution

Verified by Experts

The correct Answer is:
B
Here, `vecv_(A) = (10 hati) ms^(-1)`
`vecv_(B) = (20 cos 60^(@) hati + 20 sin 60^(@) hatj) ms^(-1)`
`=(10 hati + 10sqrt(3) hatj) ms^(-1)`

Relative velocity of B with respect to A is given by
`vecv_(BA) = vecv_(B) - vecv_(A)`
`=(10 hati + 10sqrt(3)hatj) -10hati = 10sqrt(3) hatj ms^(-1)`
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