Question

Two perpendicular rail track have two trains a and b respectively.train a moves north with a speed of 54km/hr and train B moves west with a speed of 72 km/hr assume both train starts from same point find relative velocity of a w.r.t. to b

Answer 1

The solution has. been given in the attachment

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Answer 2

Answer:

The relative velocity of A w.r.t. to B is 25 m/s in the direction of 37° North of east.

Explanation:

Given that,

Speed of train a $v_{A}=54\ km/hr=54\times\dfrac{5}{18}=15\ m/s$

Speed of train b $v_{B}=72\ km/hr=72\times\dfrac{5}{18}=20\ m/s$

Let train A moves in a north direction and let train B moves in a west direction.

So, Speed of train A is 54 km/hr and speed of train B is -72 km/hr.

Now, The relative velocity of A w.r.t to B

$\vec{v_{AB}}=\vec{v_{A}}-\vec{v_{B}}$

$\vec{v_{AB}}=15\hat{j}-(-20)\hat{i}$

$\vec{v_{AB}}=20\hat{i}+15\hat{j}$

The magnitude of the relative velocity is

$|\vec{v_{AB}}|=\sqrt{(20)^2+(15)^2}$

$|\vec{v_{AB}}|=25\ m/s$

The direction of the trains

$tan\theta = \dfrac{y-axis}{x-axis}$

$tan\theta=\dfrac{15}{20}$

$\theta = tan^{-1}\dfrac{3}{4}$

$\theta = 36.8 = 37^{\circ}$

Hence, The relative velocity of A w.r.t. to B is 25 m/s in the direction of 37° North of east.