Two cars A and B approach each other at an intersection. Car A is traveling south at 20 m/s, while car B is traveling east at 17 m/s. What is the velocity of car A as described by the passengers in car B?
A)37 m/s, eastward
B)26 m/s, 40° south of east
C)26 m/s, 50° south of east
D)26 m/s, 50° south of west
E)26 m/s, 40° south of west

Question

Quizplus · Accepted Answer

We can use vector addition to solve this problem. Let the positive x-axis point east and the positive y-axis point north. Then, the velocity of car A is (0, -20) m/s and the velocity of car B is (17, 0) m/s.

To find the velocity of car A as described by the passengers in car B, we need to find the vector sum of these velocities. Using the Pythagorean theorem, we can find the magnitude of the vector sum:

magnitude = sqrt((17)^2 + (-20)^2) = 26.1 m/s

To find the direction of the vector sum, we can use trigonometry.

tan(theta) = opposite/adjacent = (-20)/17

theta = -50.2 degrees

Since the negative sign indicates a direction south of east, the answer is:

D) 26 m/s, 50° south of west

Two Cars a and B Approach Each Other at an Intersection