Solving Two Cars Intersection Problem: Velocity of Car B Relative to Car A

[Chutzpah]

These two problems are giving me some guff. Any ideas on how to solve?

Two cars approach an intersection of perpendicular streets. Car A is moving north at 10.5 meters per second, and Car B is moving west at 17.1 meters per second. What is the velocity of Car B relative to Car A? (In other words, what is the velocity of Car B in the reference frame of Car A?)
Answer 1 -m/s
Answer 2 -° (referenced to east being 0°, all angles between 0° and 360°)

Two cars approach an intersection of perpendicular streets. Car A is moving north at 10.5 meters per second, and Car B is moving west at 17.1 meters per second. What is the velocity of Car B relative to Car A? (In other words, what is the velocity of Car B in the reference frame of Car A?)
Answer 1 m/s
Answer 2 ° (referenced to east being 0°, all angles between 0° and 360°)

 

[6Stang7]

first, if you where in car A, how would car B appear to you in frame of reference?

so think of it this way. the cars are moving as discribed; however, there is no road. instead, they are in space with nothing else around.

 

[kyle8921]

To solve this problem, we can use vector addition. We know that the velocity of Car B relative to Car A is the vector sum of their individual velocities. In this case, we can break down the velocities into their x- and y-components.

For Car A, the x-component is 0 and the y-component is 10.5 m/s. For Car B, the x-component is -17.1 m/s and the y-component is 0.

To find the velocity of Car B relative to Car A, we can use the Pythagorean theorem to calculate the magnitude of the vector, which is the square root of the sum of the squares of the x- and y-components.

So, the magnitude of the velocity of Car B relative to Car A is √(0^2 + (-17.1)^2) = 17.1 m/s.

To find the direction of this velocity, we can use the inverse tangent function to find the angle between the vector and the x-axis. In this case, the angle is 270°, since the vector points in the negative y-direction.

Therefore, the velocity of Car B relative to Car A is 17.1 m/s at an angle of 270°. This means that Car B is moving south at 17.1 m/s relative to Car A.

I hope this helps solve the problem!