Question

A motor cyclist is travelling towards north with a uniform speed of 10 ms\textsuperscript{−1} and a train is travelling towards north-west with a uniform speed of 102 ms\textsuperscript{−1}. The direction of motion of the motor cyclist as observed by a passenger in the train is

• A. East
• B. West
• C. North
• D. South

Hint:

Relative velocity = \(v_{\text{object}} - v_{\text{observer}}\). Resolve into components to find apparent direction.

Answer 1

The Correct Option is A

• Put east = +x, north = +y.
• Motorcyclist velocity: \(\vec{v}_m = (0,\,10)\) m/s.
• Train velocity (north-west) at 45° NW: \(\vec{v}_t = (-102\cos45^\circ,\,102\cos45^\circ) \approx (-72.12,\,72.12)\) m/s.
• Relative velocity (motor w.r.t. train) \(\vec{v}_{m/t} = \vec{v}_m - \vec{v}_t \approx (72.12,\,-62.12)\) m/s → vector pointing predominantly east and slightly south (i.e., south-east from train passenger viewpoint).
• Among the given options the closest single compass direction is **East** (dominant component).
• Hence option (1) East.