Question

1. Two forces of 7 lb. and 14 lb. act on a body at right angles to each other. Find the angle their resultant force makes with the force of 14 lb.

2.A velocity of 30 mph is resolved into two components, each of which makes an angle of 45 with it. Find their magnitude.

Answer 1

its basic trig :|

Answer 2

1. The resultant force is equivalent to the hypotenuse of the triangle formed by the component forces, and the angle between the result and each component is found with trig based on that premise. You're looking for the angle formed by the hypotenuse and the longer of the two sides, so the larger component is used as the adjacent side and the smaller as the opposite side. So the angle is given by the inverse tangent of 7/14, or equivalently of 1/2.

Answer 3

tan x = 7/14 = 1/2
x = arctan(1/2) = 26.56 degrees


2 components form a special 45-45 right triangle with hypotenuse of 30
both legs are magnitude of 30/sqrt2 = 15sqrt2