Question

Add the following vectors:

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.

Answer 1

1.

Consider east -west direction along the X-axis and north-south direction along Y-direction

F₁ = 200 i "i" is unit vector along X-direction

F₂ = 150 i

Net force is given as

F = F₁ + F₂ = 200 i + 150 i = 350 i

hence 350 N in east direction

2.

Since the direction of force being applied are opposite , net force is given by the difference of the two forces simply

F_net = 63 - 50 = 13 N

3.

Consider east -west direction along the X-axis and north-south direction along Y-direction

V_a = velocity of the airplane = 100 j

V_w = velocity of the wind = - 30 i

net velocity is given as

V = V_w + V_a = - 30 i + 100 j

magnitude : sqrt((- 30)² + (100)²) = 104.4 m/s

direction: = tan^-1(30/100) = 16.7 degree