Answer:
To determine the efficiency of the water slide in converting gravitational potential energy (GPE) into kinetic energy (KE), we can use the following steps:
1. **Calculate the initial gravitational potential energy (GPE):**
The gravitational potential energy at the top of the slide is given by:
\[
\text{GPE} = mgh
\]
where:
- \( m \) is the mass of the person (which will cancel out later),
- \( g \) is the acceleration due to gravity (\( 9.8 \, \text{m/s}^2 \)),
- \( h \) is the height above the water (\( 2.7 \, \text{m} \)).
2. **Calculate the final kinetic energy (KE):**
The kinetic energy when entering the water is given by:
\[
\text{KE} = \frac{1}{2} mv^2
\]
where:
- \( m \) is the mass of the person,
- \( v \) is the velocity when entering the water (\( 4.8 \, \text{m/s} \)).
3. **Calculate the efficiency:**
Efficiency is the ratio of the useful output energy (KE) to the input energy (GPE):
\[
\text{Efficiency} = \frac{\text{KE}}{\text{GPE}} \times 100\%
\]
Let's proceed with these calculations:
1. **GPE Calculation:**
\[
\text{GPE} = mgh = m \times 9.8 \, \text{m/s}^2 \times 2.7 \, \text{m} = 26.46m \, \text{J}
\]
2. **KE Calculation:**
\[
\text{KE} = \frac{1}{2} mv^2 = \frac{1}{2} m \times (4.8 \, \text{m/s})^2 = 11.52m \, \text{J}
\]
3. **Efficiency Calculation:**
\[
\text{Efficiency} = \frac{\text{KE}}{\text{GPE}} \times 100\% = \frac{11.52m \, \text{J}}{26.46m \, \text{J}} \times 100\%
\]
\[
\text{Efficiency} = \frac{11.52}{26.46} \times 100\% \approx 43.5\%
\]
So, the efficiency of the water slide in converting gravitational potential energy into kinetic energy is approximately **43.5%**.