A car is moving towards east with a speed of 25km h−1. To the driver of the car, a bus appears to move towards north with a speed of 25√3km h−1. What is the actual velocity of bus?
A
50km h−1,30∘ East of North
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B
50km h−1,30∘ North of East
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C
25km h−1,30∘ East of North
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D
25km h−1,30∘ North of East
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Solution
The correct option is A50km h−1,30∘ East of North Velocity of car,→vc=25^i Velocity of bus w.r.t car, →vb/c=25√3^j Then, →vb/c=→vb−→vc⇒→vb=→vb/c+→vc ⇒→vb=25^i+25√3^j ∣∣→vb∣∣=√252+(25√3)2=50km/h
Now, tanθ=2525√3=1√3⇒θ=30∘ Therefore direction is 30∘ East of North