To determine how far the output platform can be lifted in a hydraulic lift with an ideal mechanical advantage (IMA) of 5, we can use the relationship between the input distance and the output distance in a hydraulic system.
The ideal mechanical advantage is defined as:
\[ \text{IMA} = \frac{d_{\text{input}}}{d_{\text{output}}} \]
Where:
- \( d_{\text{input}} \) is the distance the input platform is moved (43.0 cm).
- \( d_{\text{output}} \) is the distance the output platform is lifted.
From the formula, we can express the output distance as:
\[ d_{\text{output}} = \frac{d_{\text{input}}}{\text{IMA}} \]
Substituting the given values:
\[ d_{\text{output}} = \frac{43.0 , \text{cm}}{5} \]
Calculating this gives:
\[ d_{\text{output}} = 8.6 , \text{cm} \]
Therefore, the output platform can be lifted 8.6 cm when the input platform is depressed by 43.0 cm.