A motorcycle has a velocity of 15 m/s, due south (observed by a police officer standing on the side of the road) as it passes a car with a velocity of 24 m/s, due north. The same officer observes the velocity of the car. What is the magnitude and direction of the velocity of the motorcycle as seen by the driver of the car?

$↑ 24 m / s$

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$↑ 30 m / s$

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$↓ 39 m / s$

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$↓ 40 m / s$

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Solution

The correct option is C
$↓ 39 m / s$

Velocity of the motorcycle with respect to the officer, $V_{M O} =↓ 15 m / s$

Velocity of the car with respect to the officer, $V_{C O} =↑ 24 m / s$

Velocity of the officer with respect to the car, $V_{O C} =↓ 24 m / s$

Velocity of the motorcycle with respect to the car, $V_{M C} = V_{M O} + V_{O C} = 15 m / s + 24 m / s =↓ 39 m / s$

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