Solve the problem.
-When a person bends at the waist with a straight back, the force, F, exerted by the person's lower back muscles can be estimated with the formula F = 2.89w sin (ϴ + 90°), where w is the person's
Weight, and ϴ is the angle made by the person's torso relative to the horizontal. Suppose that a
120-pound person bends at an angle of 30°. Determine the force exerted by the person's back
Muscles, and estimate the angle that requires the back muscles to exert a force of 208 pounds.
Round the force to the nearest pound, and the angle to the nearest tenth, if necessary.
A)300 pounds; 30°
B)300 pounds; 53.1°
C)26 pounds; 53.1°
D)173 pounds; 47.3°

Question

Quizplus · Accepted Answer

To find the force exerted by the person's back muscles when bending at a 30° angle, substitute w = 120 pounds and ϴ = 30° into the formula: F = 2.89 * 120 * sin(30° + 90°) = 2.89 * 120 * sin(120°). Sin(120°) is √3/2, so F ≈ 2.89 * 120 * √3/2 ≈ 300 pounds. To find the angle that requires the back muscles to exert a force of 208 pounds, set F = 208 and solve for ϴ: 208 = 2.89 * 120 * sin(ϴ + 90°). Solving this equation for ϴ gives an angle of approximately 53.1°.

Solve the Problem. -When a Person Bends at the Waist with a Straight