Kinematics - relative velocities

[srh]

Homework Statement

I have attached a picture of the situation. Small Wheels attached to the ends of rod AB roll along two surfaces. Knowing that at the instant shown the velocity vA of wheel A is 1.5 m/s to the right and the relative velocity vB/A of wheel B with respect to wheel A is perpendicular to rod AB, determine the relative velocity vB/A and velocity vB of wheel B.

Homework Equations

vA+vB/A=vA

The Attempt at a Solution

I understand that vA+vB/A =vA. I know that the component of vA is 1.5m/s in the x direction. The problems that we have done were all with right angles. I know another way to figure out the problem is to draw the vectors but we don't have all the angles. I can't seem to figure out how to find the angle that the rod AB makes w/ the x-axis. Is there a formula that I am missing? I'm just not sure where to start.

 

[berkeman]

Sorry, srh, there doesn't appear to be a picture attached. Can you please try again?

 

[piercas]

Hello,

Thank you for sharing your question and attempt at a solution. Kinematics is a fascinating and complex topic, and it is great to see students like you working hard to understand it.

To solve this problem, you can use the concept of relative velocity. Relative velocity is the velocity of one object with respect to another object. In this case, we are interested in the relative velocity of wheel B with respect to wheel A, denoted as vB/A.

To find vB/A, we can use the formula vB/A = vB - vA, where vB is the velocity of wheel B and vA is the velocity of wheel A. We know that vA = 1.5 m/s to the right, but we do not know the velocity of wheel B yet.

To find vB, we can use the fact that the relative velocity vB/A is perpendicular to the rod AB. This means that the direction of vB/A is perpendicular to the direction of vA, which is to the right. Therefore, vB must be in the y direction.

Now, we can use the Pythagorean theorem to find the magnitude of vB. We know that vA+vB/A = vA, so we can rewrite this as vB/A = -vA. This means that the magnitude of vB must be equal to the magnitude of vA, but in the opposite direction. Using the Pythagorean theorem, we can find that |vB| = |vA| = 1.5 m/s.

Therefore, vB must have a magnitude of 1.5 m/s in the y direction. This means that the velocity of wheel B is 1.5 m/s upward. To find the relative velocity vB/A, we can simply plug in the values we found for vB and vA into the formula vB/A = vB - vA. This gives us a final answer of vB/A = 1.5 m/s upward.

I hope this explanation helps you understand the concept of relative velocity and how to apply it in this problem. Keep up the good work in your studies of kinematics!