Your car is stuck in the mud and two friends are helping you. One is pulling on your car with a force of 370 N at a 40 degree angle and the other is pulling with a force of 450 N at a 30 degree angle. A force of 725 N is required to remove the car. Is the car still stuck? Please show me how to arrive at the answer.

Question

Your car is stuck in the mud and two friends are helping you.  One is pulling on your car with a force of 370 N at a 40 degree angle and the other is pulling with a force of 450 N at a 30 degree angle.  A force of 725 N is required to remove the car.  Is the car still stuck?  Please show me how to arrive at the answer.

Henry · Answer

F = 370 N @ 40 deg. + 450 N @ 30 deg.

X = hor = 370 * cos40 + 450 * cos30,
= 283.4 + 389.7 = 673.1 N.

Y = ver = 370 * sin40 + 450 * sin30,
= 237.8 + 225 = 462.8 N.

tanA = Y/X = 462.8 / 673.1 = 0.6876,
A = 34.5 deg.

F = X / cosA = 673.1/cos34.5 = 816.7N.

816.7 N > 725 N.
Therefore, the car is no longer stuck.

X and Y represent the hor and ver side of a rt triangle and F is the hyp
or Resultant.