College Physics by Openstax Chapter 3 Problem 12: Resolving Velocity Components Along Rotated Coordinate Axes

Problem:

Find the components of v_tot 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 v_tot from the rest of the other vectors, we come up with the following figure.

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)

College Physics Chapter 3 Problems

Problem 1	Problem 2	Problem 3	Problem 4	Problem 5
Problem 6	Problem 7	Problem 8	Problem 9	Problem 10
Problem 11	Problem 12	Problem 13	Problem 14	Problem 15
Problem 16	Problem 17	Problem 18	Problem 19	Problem 20
Problem 21	Problem 22	Problem 23	Problem 24	Problem 25
Problem 26	Problem 27	Problem 28	Problem 29	Problem 30
Problem 31	Problem 32	Problem 33	Problem 34	Problem 35
Problem 36	Problem 37	Problem 38	Problem 39	Problem 40
Problem 41	Problem 42	Problem 43	Problem 44	Problem 45
Problem 46	Problem 47	Problem 48	Problem 49	Problem 50
Problem 51	Problem 52	Problem 53	Problem 54	Problem 55
Problem 56	Problem 57	Problem 58	Problem 59	Problem 60
Problem 61	Problem 62	Problem 63	Problem 64	Problem 65
Problem 66	Problem 67	Problem 68	Problem 69	Problem 70