Verify That the Equation Is an Identity $F = 2.89 \mathrm { w } \sin \left( \theta + 90 ^ { \circ } \right)$

question 101

Multiple Choice

Verify that the equation is an identity.
-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 $F = 2.89 \mathrm { w } \sin \left( \theta + 90 ^ { \circ } \right)$ , where $w$ is the person's weight, and $\theta$ is the angle made by the person's torso relative to the horizontal. Suppose that a 220 -pound person bends at an angle of $30 ^ { \circ }$ . Determine the force exerted by the person's back muscles, and estimate the angle that requires the back muscles to exert a force of 381 pounds. Round the force to the nearest pound, and the angle to the nearest tenth, if necessary.

• A) 318 pounds; \(47.3 ^ { \circ }\)
• B) 551 pounds; \(30 ^ { \circ }\)
• C) 551 pounds; \(53.2 ^ { \circ }\)
• D) 26 pounds; \(53.2 ^ { \circ }\)

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Definitions:

Inspiratory Capacity

The total amount of air that can be inhaled after a normal exhalation, indicating the function of lung expansion.

Tidal Inhalation

The process of taking air into the lungs in a manner similar to the rise and fall of tides, typically in a gentle and rhythmic fashion.

Intrapulmonary Pressure

The pressure within the lung alveoli, vital for the process of breathing and gas exchange.

Pleural Cavity

The fluid-filled space between the two layers of the pleura, surrounding each lung.