Final answer:
The ideal mechanical advantage of the incline being 4.0 for a 15 m tall pyramid implies a length of the incline of 60 m. Using trigonometry, the angle of the incline that would produce such an advantage is approximately 14 degrees. Therefore, the closest option from those provided is 14.5 degrees, making option (a) the correct answer.
Step-by-step explanation:
When building the ancient pyramids, the use of inclines or ramps significantly reduced the force required to lift heavy materials to great heights. If an incline has an ideal mechanical advantage (IMA) of 4.0 and the pyramid is 15 m tall, to determine the angle of the incline, we need to calculate the length of the incline that would provide that mechanical advantage and then use trigonometry to find the angle.
Firstly, the IMA of an incline is given by the formula:
IMA = length of incline / height of incline
If the IMA is 4.0 and the height is 15 m, then the length of the incline is:
Length = 4.0 × 15 m = 60 m
We now use the tangent function, where:
= angle of incline
Tan() = height / length
Tan() = 15 m / 60 m
Tan() = 0.25
Therefore, ≈ 14 degrees.
The closest angle to our result from the given options would be 14.5 degrees. Hence, the correct answer is (a) 14.5 degrees.