Question

A car is going eastwards with a velocity of $8m{s}^{-1}$. A train appears to be moving northwards with a velocity $15m{s}^{-1}$ relative to the passenger in the car. What is the actual velocity of the train?

• A. $7m{s}^{-1}$
• B. $17m{s}^{-1}$
• C. $23m{s}^{-1}$
• D. None of the above

Answer 1

Answer: (B)

$17m{s}^{-1}$

Relative to the car (Which is moving east)
The train appears to be moving only north.
This implies that the train relative to the ground is moving the same velocity east as the car.
i.e.,
$V_{train}=15\left(north\right)+8\left(east\right)$
$V_{train}=\sqrt{{15}^2+8^2}=17m{s}^{-1}$
Hence option $C$ is correct.