A warehouse worker uses a forkift to lift a crate of pickles on a platform to a height 2.75 m above the floor. The combined mass of the platform and the crate is 207 kg. If the power expended by the forklift is 1440 W, how long does it take to lift the crate ?

Options

A. 37.2s
B. 3.87s
C. 1.86s
D. 5.81s

Answer

To solve the problem, we need to determine how long it takes for the forklift to lift the crate of pickles to a height of 2.75 m, given the power output of the forklift and the mass of the crate and platform.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Height (h) = 2.75 m
- Mass (m) = 207 kg
- Power (P) = 1440 W

2. **Calculate the Work Done (W):**
The work done against gravity to lift the crate can be calculated using the formula:
\[ W = m \cdot g \cdot h \]
where \( g \) (acceleration due to gravity) is approximately \( 9.81 \, \text{m/s}^2 \). For simplicity, we can use \( g \approx 10 \, \text{m/s}^2 \).

Substituting the values:
\[ W = 207 \, \text{kg} \cdot 10 \, \text{m/s}^2 \cdot 2.75 \, \text{m} \]
\[ W = 2070 \cdot 2.75 = 5692.5 \, \text{J} \]

3. **Use the Power Formula to Find Time (t):**
Power is defined as the work done per unit time:
\[ P = \frac{W}{t} \]
Rearranging this gives:
\[ t = \frac{W}{P} \]

Substituting the values we found:
\[ t = \frac{5692.5 \, \text{J}}{1440 \, \text{W}} \]
\[ t \approx 3.95 \, \text{s} \]

4. **Final Answer:**
The time taken to lift the crate is approximately \( 3.95 \) seconds.