Find the necessary quantities if the given changes are made in the indicated examples of this section.

In Example 2, find the resultant location if the 41.25° angle is changed to 31.25°.

Data from Example 2

A ship sails 32.50 mi due east and then turns 41.25° north of east. After sailing another 16.18 mi, where is it with reference to the starting point?

In this problem, we are to find the resultant displacement of the ship from the two given displacements. The problem is diagrammed in Fig. 9.33, where the first displacement is labeled vector A and the second as vector B. Because east corresponds to the positive x-direction, note that the x-component of the resultant is A + B_x and the y-component of the resultant is B_y. Therefore, we have the following results:

Therefore, the ship is 45.92 mi from the starting point, in a direction 13.44° north of east.

R = A + B = 32.50 +16.18 cos 41.25 = 32.50+ 12.16 = 44.66 mi R 16.18 sin 41.25 = 10.67 mi R = (44.66) + (10.67) = 8 tan 10.67 44.66 13.44 45.92 mi