College Physics by Openstax Chapter 3 Problem 12

Find the components of vtot along a set of perpendicular axes rotated 30º counterclockwise relative to those in Figure 3.55.

The figure shows v_A directed 22.5° from the positive x-axis, and v_B started from the head of v_A and is directed 23.0° from the resultant. The resultant is given to be 6.72 m/s and is directed 26.5° from v_A. In total, the resultant is measured 49° from the positive x-axis.
Figure 3.55

Solution:

By isolating the vtot from the rest of the other vectors, we come up with the following figure.

The isolated resultant velocity

The resultant velocity has a magnitude of 6.72 m/s and is directed 49° from the positive x-axis. Now, we shall create another set of axes rotated at 30° counterclockwise. We call the axes x’ and y’ axes. The figure is shown below.

The resultant velocity with the rotated axes.

From the figure, we can see that the resultant velocity is 19° from the x’ axis. Therefore, the x’ and y’ components are:

\text{x'-component}=\left(6.72\:\text{m/s}\right)\cos 19^{\circ} =6.35\:\text{m/s}\ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)
 \text{y'-component}=\left(6.72\:\text{m/s}\right)\sin 19^{\circ} =2.19\:\text{m/s}\ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)
Advertisements
Advertisements