Question

The car is moving towards the east with a speed of $25km/h$ . To the driver of the car, a bus appears to move towards the north with a speed of $25\sqrt 3 km/h$ . What is the actual velocity of the bus?
(A) $50km/h,{30^ \circ }$ East of north
(B) $50km/h,{30^ \circ }$ North of east
(C) $25km/h,{30^ \circ }$ East of north
(D) $25km/h,{30^ \circ }$ North of east.

Answer 1

Hint : To solve this question, we have to know about the velocity and the relative velocity. We know that The relative velocity is the speed or the velocity of an item or onlooker B in the rest edge of another article or spectator A, on the off chance that it is steady, where is A's speed in the rest edge of B. Relative velocity is by and large used to portray the movement of planes in the breeze or moving boats through water and so on This speed is figured by the individual as a spectator inside the article or the object.

Complete Step By Step Answer:
Let us consider that, ${V_b} =$ velocity of bus.
Again, ${V_c} =$ velocity of car
${V_{bc}} =$ $25\sqrt 3 km/h$ (According to the question)
Now, we know that, according to the definition of the relative velocity,
$\left| {{{\vec V}_b}} \right| = \sqrt {{{(25)}^2} + {{(25\sqrt 3 )}^2}}$
Or, $\left| {{{\vec V}_b}} \right| = 50km/h$
Now, for the direction, we have to calculate the $\tan \theta$
$\tan \theta$ $= \frac{{25\sqrt 3 }}{{25}} = \sqrt 3$
So, here we can say that, theta is from the east direction. Therefore it will be at ${30^ \circ }$ east of north.
So, we can say the right answer is option A.

Note :
This is a question of relative velocity, one may get confused between actual and relative velocities. The questions may be different by changing the magnitude of velocity and the direction of vehicles approaching in similar or opposite directions. Also needs to be careful regarding directions as well.