Vector Worksheet Answer Key

1. (a) 5 mph

(b) 15 mph

2. Because the tread is moving in the opposite direction at 5 mph. The total velocity is therefore zero.

3. (a) V² = 12² + 5² = 14400 + 2500 = 16900.     V = 130 mph.

(b) tan x = 5/12 = 0.41667; using the "tan^–1" button on the calculator, x = 22.62 deg.
Or if you prefer: sin x = 5/13 = 0.384615, using "sin^–1" , same result. "

4. (a) To represent it as the sum of two other vectors--usually, in prescribed directions.

(b) Because the directions of the air speed and wind speed may have odd angles. Rather than deal with those angles, it is easier to resolve each into a north-south and an east-west component, add up the components in each direction (like numbers) and then form the sum again.

5. Due north at 79.32 mph. Let V be the airplane's velocity, W the wind's velocity, and let us resolve these vectors in an (x,y) system with the x-axis pointing due east and the y axis due north. The components are:

V_x=-120 sin 17.13°= -35.36     V_y=120 cos 17.32° = 114.68
W_x= 50 cos 45° = 35.36         W_y= -50 sin 45°= - 35.36

The x-components cancel, the total y-component is
114.68-35.36 = 79.32

6. They have to overcome the component of the weight parallel to the surface of the ramp, which is 1000*sin 5° = 87.15 kg.