What Is the Speed of the Center of Mass for Two Cars Traveling Perpendicularly?

[Alex Wiseman]

Homework Statement

Two cars leave the same point at the same time, each traveling at the same constant speed of 89.0 km/h and each having the same mass. However, the first car drives directly east, while the second car heads directly south. At what speed (the magnitude of the velocity) is the centre of mass of these two cars travelling? Give your answer as a positive value in m/s (without a sign).

Homework Equations

I have attempted this using trigonometry, but have yet to come up with an answer that is correct.

The Attempt at a Solution

89 km/h = 24.72m/s

Car 1: 24.72m/s [E]
Car 2: 24.72m/s

I have tried vector addition, and sin law. Any suggestions?

Never mind it's been figured out.

sin45(24.72)/sin90 = 17.479m/s -> magnitude of the cars speed.

 

[anathema]

First, it is important to note that the mass of the cars is not relevant in this problem, as the center of mass is only affected by the velocities of the objects involved.

To solve this problem, we can use the concept of vector addition. The center of mass of the two cars will be the point that is equidistant from both cars. Since the cars are traveling at the same speed, the center of mass will also be moving at the same speed.

To find the magnitude of the velocity of the center of mass, we can use the Pythagorean theorem. The velocity of car 1 (traveling east) can be represented by a vector with a magnitude of 24.72 m/s in the positive x-direction. The velocity of car 2 (traveling south) can be represented by a vector with a magnitude of 24.72 m/s in the negative y-direction.

Using the Pythagorean theorem, we can find the magnitude of the velocity of the center of mass:

v = √(24.72^2 + (-24.72)^2) = √1224.5184 = 34.99 m/s

Therefore, the center of mass of the two cars is traveling at a speed of 34.99 m/s.