Question

When in going east at 10 km/h a train moving with constant velocity appears to be moving exactly north - east. when my velocity is increased to 30 km/h east it appears to be moving north.

At what speed (in Kmph) should I move North so that train appears to be moving exactly South-East?

• A. 30 km/h
• B. 20 km/h
• C. 50 km/h
• D. 10 km/h

Answer 1

The correct option is B 20 km/h

We know that,

The train appears to be moving exactly toward north east when speed of observer is $10km/h$towards east.

Now, the angle made by train with the direction of east is ${45}^0$

Therefore, the speed of train along

the direction of north

$v_n=v\sin {45}^0$

$v_n=10\times 1$

$v_n=10km/h$

Now, the direction of east

$v_e=v\sin {45}^0$

$v_e=10\times 1$

$v_e=10km/h$

Now, the actual speed of train is

$v=\sqrt{v_n^2+v_e^2}$

$v=\sqrt{{10}^2+{10}^2}$

$v=10\sqrt{2}km/h$

Now,

Let the speed of observer towards the direction of north be $v_0$to observe that train moves exactly towards south –east

Therefore,

$\frac{v}{v_0}=\cos {45}^0$

$v_0=\frac{v}{\cos {45}^0}$

$v_0=10\sqrt{2}\times \sqrt{2}$

$v_0=2\times 10$

$v_0=20km/h$

Hence, the speed of observer is $20km/h$