Analyzing the Test Launch Data
A data table showing the results of a simulated projectile launch at a constant initial speed but with varying launch angles from 15 to 75 degrees. A target is located at a specific distance, for example, 78 meters.
- According to the dataset, which launch angle produced the maximum range?
- Identify two different launch angles from the table that produced nearly the same range. What is the mathematical relationship between these two angles?
- [SEP] Calculate the percent change in range when the angle is increased from 15 to 30 degrees. Then, calculate the percent change when the angle is increased from 60 to 75 degrees. How does this quantitative analysis strengthen the claim that the effect of changing the angle is not linear?
Calculating the Solution
A data table showing the results of a simulated projectile launch at a constant initial speed but with varying launch angles from 15 to 75 degrees. A target is located at a specific distance, for example, 78 meters.
- The target is located at 78 m, a distance not achieved by any of the test launches. Using the unit's key formulas, you will now calculate the ideal launch angle. First, assume a launch angle of 40 degrees. What would the initial horizontal (v_0x) and vertical (v_0y) velocities be? [BACKGROUND KNOWLEDGE: Resolving a velocity vector into its components requires trigonometry: v_0x = v_0 cos(θ) and v_0y = v_0 sin(θ).]
- Using your calculated v_0y, determine the total time the projectile would be in the air.
- Using the total time and v_0x, calculate the range for your 40-degree test launch. How does it compare to the target distance of 78 m? Based on this result, should your next attempt use a higher or lower angle? Explain your reasoning.
- [SEP] The dataset was generated by a simulation that ignores air resistance. What is a key limitation of using this simulation to make predictions in the real world? How would the presence of air resistance likely affect the measured range compared to the calculated range?
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