Question

Car 1 drives 35 mph to the east, and car 2 drives 50 mph to the west. From the frame of reference of car 1, what is the velocity of car 2?

A. 85 mph west
B. 15 mph east
C. 85 mph east
D. 15 mph west

Answer 1

The distance between the two cars is increasing at the rate of 85 mph.

A passenger in Car-1 says that he is at rest in his own frame of reference,
and Car-2 is moving away from him at 85 mph, toward the west.

Answer 2

A. 85 mph west

Step-by-step explanation:

Velocity of car 1 is given as

`v_1 = 35 mph` towards East

`\vec v_1 = 35(-\hat i) mph`

Velocity of car 2 is given as

`v_2 = 50 mph` towards West

`\vec v_2 = 50 (\hat i) mph`

Now we need to find the speed of car 2 with respect to the frame of car 1

so it is given as

`\vec v_(21) = \vec v_2 - \vec v_1`

now we will have

`\vec v_(21) = 50 (\hat i) - 35 (-\hat i) = 85 \hat i`

so the relative speed will be 85 mph towards West