Final answer:
The angle of the hill with the horizon is found by using the trigonometric relationship sin(θ) = opposite/hypotenuse. By calculating the inverse sine (arcsin) of the force required to keep the cart in place (33 pounds) divided by the cart's weight (115 pounds), the angle is determined to be approximately 16.26 degrees.
Step-by-step explanation:
The question is asking to find the angle of a hill with the horizon, given that a 115-pound cart requires 33 pounds of force to keep it in place. To find the angle of the hill, we can use the concept of forces on an inclined plane. The force required to keep the cart in place is the component of the weight of the cart acting down the slope. The weight of the cart can be calculated as the mass times the acceleration due to gravity (g = 9.8 m/s2), which gives us the force in Newtons. Since we have the force in pounds, we will treat it as the force directly.
To find the angle, θ, we use the trigonometric relationship: sin(θ) = opposite/hypotenuse. In this case, the opposite side is the force keeping the cart in place (33 pounds), and the hypotenuse is the weight of the cart (115 pounds). This yields sin(θ) = 33/115.
To find the angle θ, we take the inverse sine (also known as arcsin) of 33/115:
θ = arcsin(33/115)
θ ≈ 16.26 degrees
Therefore, the angle of the hill with the horizon is approximately 16.26 degrees, which corresponds to option a).