# Vector Addition and Subtraction

## Problems

### practice

- Two people are pushing a disabled car. One exerts a force of 200 N east, the other a force of 150 N east. What is the net force exerted on the car? (Assume friction to be negligible.)
- Two soccer players kick a ball simultaneously from opposite sides. Red #3 kicks with 50 N of force while Blue #5 kicks with 63 N of force. What is the net force on the ball?
- An airplane heads due north at 100 m/s through a 30 m/s cross wind blowing from the east to the west. Determine the resultant velocity of the airplane (relative to due north).
- A mountain climbing expedition establishes a base camp and two intermediate camps, A and B. Camp A is 11,200 m east of and 3,200 m above base camp. Camp B is 8400 m east of and 1700 m higher than Camp A. Determine the displacement between base camp and Camp B.

### numerical

- A plane heads east with a velocity of 52 m/s through a 12 m/s cross wind blowing the plane south. Find the magnitude and direction of the plane's resultant velocity (relative to due east).
- An ambitious hiker walks 25 km west and then 35 km south in a day. Find the magnitude and direction of the hiker's resultant displacement (relative to due west).
- A boat heads directly across a river with a velocity of 12 m/s. If the river flows at 6.0 m/s find the magnitude and direction of the boat's resultant velocity. (State the direction relative to an imaginary line drawn straight across the river.)
- I went for a walk the other day. I went four avenues east (0.80 miles), then twenty-four streets south (1.20 miles), then one avenue west (0.20 miles), and finally eight streets north (0.40 miles).
- What distance did I travel?
- What's my resultant displacement (magnitude and direction relative to due east)?

- A plane intends to fly north with a speed of 250 m/s relative to the ground through a high altitude cross wind of 50 m/s coming from the east. Determine…
- the bearing that the plane should take (relative to due north)
- the plane's speed with respect to the air

### algebraic

- At a particular instant, a stationary observer on the ground sees a package falling from a moving airplane with a speed
*v*at an angle θ to the vertical. To the pilot flying horizontally at a constant speed relative to the ground the package appears to be falling vertically with a speed_{observer}*v*at that same instant. What is the speed of the pilot relative to the ground in terms of the given quantities?_{pilot}

### graphical drill

- worksheet-addition.pdf

Determine the magnitude (in centimeters) and direction (in standard form) of the resultant vector**B**+**A**for each of the combinations below. Measure its length in centimeters and direction angle in standard form (i.e.; right 0°, up 90°, left 180°, down 270°, etc.). Use the horizontal reference lines as needed. - worksheet-subtraction.pdf

Determine the magnitude (in centimeters) and direction (in standard form) of the resultant vector**B**−**A**for each of the combinations below. Measure its length in centimeters and direction angle in standard form (i.e.; right 0°, up 90°, left 180°, down 270°, etc.). Use the horizontal reference lines as needed.