10.8.4. Applications of Vectors

A car is moving on a straight road with a velocity of km/h, while another car is moving on the same road with a velocity of km/h. Given that is the unit vector in the direction of movement of the first car, determine the relative velocity of the first car with respect to the second one knowing that both cars are moving in the same direction.

• Akm/h
• Bkm/h
• Ckm/h
• Dkm/h

Example

A car is moving on a straight road with a velocity of km/h, while another car is moving on the same road with a velocity of km/h. Given that is the unit vector in the direction of movement of the first car, determine the relative velocity of the first car with respect to the second one knowing that both cars are moving in the same direction.

Solution

Since is the unit vector in the direction of the movement of the first car, represent the actual velocity of the first car as km/h, and the actual velocity of the second car, which is moving in the same direction, as km/h. The relative velocity of a body with respect to another body , or , is the velocity at which it seems body moves. Find as follows:

Thus, the relative velocity of the first car with respect to the second one is km/h.

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