Answer:
Step-by-step explanation:
To calculate the range, we can use the kinematic equation:
Range = (velocity^2 * sin(2θ)) / g
where,
velocity = calculated velocity (m/s)
θ = angle of launch (assumed to be 45 degrees in this case)
g = acceleration due to gravity (approximately 9.81 m/s^2)
Let's calculate the predicted range and percent error for each ramp distance:
1. For a ramp distance of 0.27m and a calculated velocity of 1.35 m/s:
Range = (1.35^2 * sin(2 * 45°)) / 9.81
Range ≈ (1.8225 * 1) / 9.81
Range ≈ 0.186 meters
Percent Error = |(Average Actual Range - Predicted Range) / Average Actual Range| * 100
Percent Error = |(0.27 - 0.186) / 0.27| * 100
Percent Error ≈ |0.084 / 0.27| * 100
Percent Error ≈ 0.311 * 100
Percent Error ≈ 31.1%
2. For a ramp distance of 0.16m and a calculated velocity of 1.04 m/s:
Range = (1.04^2 * sin(2 * 45°)) / 9.81
Range ≈ (1.0816 * 1) / 9.81
Range ≈ 0.110 meters
Percent Error = |(Average Actual Range - Predicted Range) / Average Actual Range| * 100
Percent Error = |(0.16 - 0.110) / 0.16| * 100
Percent Error ≈ |0.05 / 0.16| * 100
Percent Error ≈ 0.3125 * 100
Percent Error ≈ 31.25%
3. For a ramp distance of 0.04m and a calculated velocity of 0.52 m/s:
Range = (0.52^2 * sin(2 * 45°)) / 9.81
Range ≈ (0.2704 * 1) / 9.81
Range ≈ 0.028 meters
Percent Error = |(Average Actual Range - Predicted Range) / Average Actual Range| * 100
Percent Error = |(0.04 - 0.028) / 0.04| * 100
Percent Error ≈ |0.012 / 0.04| * 100
Percent Error ≈ 0.3 * 100
Percent Error ≈ 30%
Please note that the "Predicted Range" is calculated based on the assumption that the launch angle is 45 degrees, as this angle is not specified in the data. The "Percent Error" represents the deviation between the calculated range and the average actual range provided in the table.