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25° 30 35° 40° 45° 50° 55° 60° 65° 70° 75° 80° 85° Ax 17.5 19.4 21.5 22.5 22.9 22.5 21.5 19.8 17.5 14.7 11.4 7.8 3.9 7 4 9 4 4 8 Time of flight for 45°: 2.16s Range vs. Initial Launch Angle 25 20 E 15 10 Range (m)

25° 30 35° 40° 45° 50° 55° 60° 65° 70° 75° 80° 85° Ax 17.5 19.4 21.5 22.5 22.9 22.5 21.5 19.8 17.5 14.7 11.4 7.8 3.9 7 4 9 4 4 8 Time of flight for 45°: 2.16s Range vs. Initial Launch Angle 25 20 E 15 10 Range (m)

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### Projectile Motion Educational Page #### Table 1: Even Plane Height (y = 0) | Initial Launch Angle (°) | 25° | 30° | 35° | 40° | 45° | 50° | 55° | 60° | 65° | 70° | 75° | 80° | 85° | |--------------------------|------|------|------|------|------|------|------|------|------|------|------|------|------| | Δx (m) | 17.5 | 19.4 | 21.5 | 22.5 | 22.9 | 22.5 | 21.5 | 19.8 | 17.5 | 14.7 | 11.4 | 7.8 | 3.9 | | Error (m) | 7 | 9 | 5 | 9 | 4 | 9 | 5 | 6 | 7 | 4 | 7 | 4 | 8 | **Time of flight for 45°: 2.16s** #### Graph: Range vs. Initial Launch Angle The graph displays the relationship between the projectile range (in meters) and the initial launch angle (in degrees). The x-axis represents the initial launch angle (in degrees), ranging from 0 to 90 degrees. The y-axis shows the range (in meters), ranging from 0 to 25 meters. The plotted points illustrate the range achieved at each launch angle. 1. At approximately 25°, the range is about 17.5 meters. 2. The range increases as the angle increases, peaking near 45° with a range close to 22.9 meters. 3. After 45°, the range decreases, reaching about 3.9 meters at 85°. #### Calculation Task 2. **Using the equation \( y = y_i + v_{yi}t - \frac{1}{2}gt^2 \), calculate the time of flight for the initial launch angle of 45°.** This educational page provides the necessary data and visual representation to understand the impact of launch angles on projectile motion range and invites students to further analyze the projectile
Transcribed Image Text:### Projectile Motion Educational Page #### Table 1: Even Plane Height (y = 0) | Initial Launch Angle (°) | 25° | 30° | 35° | 40° | 45° | 50° | 55° | 60° | 65° | 70° | 75° | 80° | 85° | |--------------------------|------|------|------|------|------|------|------|------|------|------|------|------|------| | Δx (m) | 17.5 | 19.4 | 21.5 | 22.5 | 22.9 | 22.5 | 21.5 | 19.8 | 17.5 | 14.7 | 11.4 | 7.8 | 3.9 | | Error (m) | 7 | 9 | 5 | 9 | 4 | 9 | 5 | 6 | 7 | 4 | 7 | 4 | 8 | **Time of flight for 45°: 2.16s** #### Graph: Range vs. Initial Launch Angle The graph displays the relationship between the projectile range (in meters) and the initial launch angle (in degrees). The x-axis represents the initial launch angle (in degrees), ranging from 0 to 90 degrees. The y-axis shows the range (in meters), ranging from 0 to 25 meters. The plotted points illustrate the range achieved at each launch angle. 1. At approximately 25°, the range is about 17.5 meters. 2. The range increases as the angle increases, peaking near 45° with a range close to 22.9 meters. 3. After 45°, the range decreases, reaching about 3.9 meters at 85°. #### Calculation Task 2. **Using the equation \( y = y_i + v_{yi}t - \frac{1}{2}gt^2 \), calculate the time of flight for the initial launch angle of 45°.** This educational page provides the necessary data and visual representation to understand the impact of launch angles on projectile motion range and invites students to further analyze the projectile
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