Question

A rope is pulling a 320-pound box up an incline that's 16 feet long. If 80 pound of force is used to move the box up the incline, how tall is the incline?

a.)6 feet
b.)10 feet
c.)4 feet
d.)8 feet

Answer 1

The height of the incline can be found by setting up a proportional relationship using the force to move the box and the weight of the box. After simplifying, it's determined that the height of the incline is 4 feet.

Step-by-step explanation:

The question at hand is a physics problem that can be solved using principles from mathematics, specifically trigonometry or the concept of similar triangles. To find the height of the incline, one must use the relationship between the length of the incline (the hypotenuse in this context), the height (the opposite side), and the force used to move the box (which can give us a ratio similar to the slope of the incline).

Since the horizontal length of the incline is not changing, and assuming a constant slope, the ratio of the force to pull the box up (80 pounds) to the weight of the box (320 pounds) should be equivalent to the ratio of the height of the incline to the length of the incline (16 feet). Therefore, we can set up a proportional relationship:

80/320 = height/16

When you solve for the height, you get:

height = (80/320) * 16

height = 1/4 * 16

height = 4 feet

So, the answer is (c) 4 feet.