The Physics
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Opus in profectus

Vector Addition & Subtraction

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Problems

practice

  1. 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.)
  2. 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?
  3. 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).
  4. 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 8,400 m east of and 1,700 m higher than Camp A. Determine the displacement between base camp and Camp B.

numerical

  1. 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).
  2. 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).
  3. 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.)
  4. 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).
    1. What distance did I travel?
    2. What's my resultant displacement (magnitude and direction relative to due east)?
  5. 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…
    1. the bearing that the plane should take (relative to due north)
    2. the plane's speed with respect to the air

algebraic

  1. At a particular instant, a stationary observer on the ground sees a package falling from a moving airplane with a speed vobserver 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 vpilot at that same instant. What is the speed of the pilot relative to the ground in terms of the given quantities?

worksheets

  1. 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.
  2. 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.