Vector Addition & Subtraction

Practice

practice problem 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.)

solution

practice problem 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?

solution

practice problem 3

An airplane flies 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.

solution

practice problem 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.

solution

Add vectors in the same direction with "ordinary" addition.

x = 11,200 m + 8,400 m = 19,600 m
y = 3,200 m + 1,700 m = 4,900 m

Add vectors at right angles with a combination of pythagorean theorem for magnitude …

r = √(x2 + y2) = √[(19,600 m)2 + (4,900 m)2]
 = 20,200 m

and tangent for direction.

tan θ =  y  =  4,900 m  ⇒  θ = 14.0°
x 19,600 m

Don't forget to answer the question.

Camp B is 20,200 m away from base camp at an angle of elevation of 14.0°.

Oh yeah, and don't forget to make a drawing. I probably should have told you to do that earlier.


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