Question

after climbing a steep hill, a camper uses a rope to pull their gear to the top. the incline has an ideal mechanical advantage of 1.5. find the height of the hill. the length of the incline (the rope) is 100 (unit not specified, assume a length unit like meters or feet).

Explanation:

Step1: Recall IMA formula for incline

The Ideal Mechanical Advantage (IMA) of an inclined plane is given by the formula \( IMA=\frac{\text{Length of incline (L)}}{\text{Height of incline (h)}} \). Here, the length of the incline \( L = 100 \) (assuming the unit is consistent, like meters or feet) and \( IMA = 1.5 \). We need to solve for \( h \).

Step2: Rearrange the formula to solve for h

From \( IMA=\frac{L}{h} \), we can rearrange it to \( h=\frac{L}{IMA} \).

Step3: Substitute the values

Substitute \( L = 100 \) and \( IMA = 1.5 \) into the formula: \( h=\frac{100}{1.5}=\frac{100\times2}{3}=\frac{200}{3}\approx 66.67 \) (depending on the unit, if the length was in a unit like meters, the height will be in the same unit).

Answer:

\( h=\frac{200}{3}\approx 66.67 \) (unit same as the length of incline, e.g., if length was in meters, height is in meters)