To determine the trial during which the rock reached the highest point above the ground, we'll use the relationship between the mechanical energy, gravitational potential energy, and height. Specifically, gravitational potential energy (PE) is given by:
[tex]\[ PE = m \cdot g \cdot h \][/tex]
where:
- \( m \) is the mass of the rock,
- \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)),
- \( h \) is the height above the ground.
Rearranging the formula to solve for \( h \) gives us:
[tex]\[ h = \frac{PE}{m \cdot g} \][/tex]
Given the mass \( m = 2 \, \text{kg} \) and looking at the mechanical energy for each trial, we can calculate the height \( h \):
For Trial 1:
- Mechanical Energy = \( 176.4 \, \text{J} \)
- \( h_1 = \frac{176.4}{2 \cdot 9.8} = \frac{176.4}{19.6} = 9.0 \, \text{m} \)
For Trial 2:
- Mechanical Energy = \( 157.7 \, \text{J} \)
- \( h_2 = \frac{157.7}{2 \cdot 9.8} = \frac{157.7}{19.6} \approx 8.045918367 \, \text{m} \)
For Trial 3:
- Mechanical Energy = \( 170.2 \, \text{J} \)
- \( h_3 = \frac{170.2}{2 \cdot 9.8} = \frac{170.2}{19.6} \approx 8.683673469 \, \text{m} \)
For Trial 4:
- Mechanical Energy = \( 123.7 \, \text{J} \)
- \( h_4 = \frac{123.7}{2 \cdot 9.8} = \frac{123.7}{19.6} \approx 6.311224490 \, \text{m} \)
Now we compare the calculated heights to find the trial during which the rock reached the highest point. The heights for the trials are:
- Trial 1: \( 9.0 \, \text{m} \)
- Trial 2: \( 8.045918367 \, \text{m} \)
- Trial 3: \( 8.683673469 \, \text{m} \)
- Trial 4: \( 6.311224490 \, \text{m} \)
The highest height is \( 9.0 \, \text{m} \) from Trial 1.
So, the rock was the highest above the ground during:
- Trial 1
