You are participating in the Iditarod, and your sled dogs are pulling you across a frozen lake with a force of 1550 N while a 200 N wind is blowing at you at 150 degrees from your direction of travel. What is the net force (magnitude in newtons and direction in degrees from your direction of travel)? (Give the smallest angle between the direction of travel and the direction of the net force. Assume that you are traveling in the +x-direction and that the wind is blowing from the second quadrant of the xy-plane.)

The answer to the question is

The net force (magnitude in newtons and direction in degrees from your direction of travel) is 1726.104 N ∡ 3.315 ° clockwise or 356.685° counterclockwise from the direction of travel.

Explanation:

The net force is given by

The force of pull by the dogs = 1550 N

Direction of force of pull by the dogs = 0° from the x axis

The force of the wind = 200 N

Direction of wind force = 150 ° from the x axis

Therefore x component of the wind force = 200 cos 30 =173.205 N

y component of the wind force = 200 sin 30 = 100 N

Summing the forces in the x and y direction gives

∑Fx = 1550 +173.205 = 1723.205 N

∑Fy = 100 N

Therefore the resultnt force on the Iditarod competitor is given by

√((∑Fx)²+(∑Fy)²) = √((1723.205)²+(100)²) = 1726.104 N and the direction is

=   =3.315 ° in the x, -y plane

c. magnitude and direction