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.

 

[radou]

This thread belongs to the homework section.

You should do some google-ing on vectors and learn more, instead of thinking about missing formulas. Btw, you can solve this graphically too, of course.

 

[piercas]

Hello, thank you for your question. Kinematics, specifically relative velocities, can be a tricky concept to grasp, especially when dealing with angles and vectors. It's important to remember that velocity is a vector quantity, meaning it has both magnitude and direction. In this situation, the velocity of wheel A is given as 1.5 m/s to the right, which means it has a magnitude of 1.5 m/s and a direction of the positive x-axis.

To find the relative velocity of wheel B with respect to wheel A, we can use the formula vB/A = vB - vA. Since we know that vA = 1.5 m/s to the right, we can substitute that into the formula to get vB/A = vB - 1.5 m/s.

To find the velocity of wheel B, we need to know the magnitude and direction of vB. We can use the Pythagorean theorem to find the magnitude, which is the square root of the sum of the squares of the components. In this case, the components are the x and y components of vB. Since we know that vB/A is perpendicular to rod AB, we can use basic trigonometry to find the y component, which is the opposite side of the right triangle formed by vB and vB/A.

As for finding the angle that rod AB makes with the x-axis, we can use the inverse tangent function (tan^-1) to find the angle. The tangent of an angle is equal to the opposite side divided by the adjacent side, which in this case would be the y component of vB/A divided by the x component of vB/A.

I hope this helps guide you in solving the problem. Remember to always break down the given information, use applicable formulas, and utilize basic trigonometry to find missing components. Good luck!