Question

On a straight, level, two-lane road, two cars moving in opposite directions approach and pass each other. Car A is in the eastbound lane moving with a speed of 11 m/s, and Car B is in the westbound lane moving with a speed of 31 m/s.
(a) What is the magnitude and direction of the velocity of car A as seen by the driver of car B? magnitude m/s direction
(b) What is the magnitude and direction of the velocity of car B as seen by the driver of car A? magnitude m/s direction

Answer 1

Answer:

a) 42 m/s, positive direction (to the east), b) 42 m/s, negative direction (to the west).

Explanation:

a) Let consider that Car A is moving at positive direction. Then, the relative velocity of Car A as seen by the driver of Car B is:

$\vec v_{A/B} = \vec v_{A} - \vec v_{B}\\\vec v_{A/B} = 11 \frac{m}{s} \cdot i + 31 \frac{m}{s} \cdot i\\\vec v_{A/B} = 42 \frac{m}{s} \cdot i$

42 m/s, positive direction (to the east).

b) The relative velocity of Car B as seen by the drive of Car A is:

$\vec v_{B/A} = \vec v_{B} - \vec v_{A}\\\vec v_{B/A} = -31 \frac{m}{s} \cdot i - 11 \frac{m}{s} \cdot i\\\vec v_{B/A} = - 42 \frac{m}{s} \cdot i$

42 m/s, negative direction (to the west).