Practice 3A: | 1 | 2 | 3 | 4 | Go up
Finding resultant magnitude and direction

1. A truck driver attempting to deliver some furniture travels 8 km east, turns around and travels 3 km west, and then travels 12 km east to his destination.

a. What distance has the driver traveled?

Here's what you know, Dx1 = 8 km, Dx2 = -3 km, and Dx3 = 12 km. Add the absolute value of the three distances to get the total distance traveled, so 8 km + 3 km + 12 km = 23 km.

b. What is the driver's total displacement?

Here's what you know, Dx1= 8 km, Dx2 = -3 km, and Dx3 = 12 km. Since all vectors are on the same line (x-axis), add all the magnitudes to get the total displacement: 8 km + -3 km + 12 km = 17 km to the east (since 17 is positive).

2. While following the directions on a treasure map a pirate walks 45.0 m north, then turns and walks 7.5 m east. What single straight-line displacement could the pirate have taken to reach the treasure?

Here's what you know, Dy = 45.0 m, and Dx = 7.5 m. Use the formula d = (Dx^2 + Dy^2)^0.5 and plug in: d = (7.5^2 + 45.0^2)^0.5, so d = 45.6207189772 m = 46 m (significant digits). Use the formula q = tan-1( Dy / Dx ) and plug in: q = tan-1( 45.0 m / 7.5 m ), so q = 80.537677792 deg = 81 deg (significant digits). Yeilding, 46 m at 81 deg north of east.