To determine Brad's position on the Ferris wheel at points B and E, we need to analyze the movement of the wheel.

Key Information

• Diameter of the Ferris wheel: 30 meters (radius = 15 meters)
• Height of the platform: 8 feet (approximately 2.44 meters)
• Total ride time: 20 minutes
• Total revolutions: 5 revolutions

Calculating Angular Speed

1. Total time of ride in seconds: $20 \text{ minutes} = 20 \times 60 = 1200 \text{ seconds}$
2. Angular speed (in radians per second): $\text{Total angle} = 5 \times 2\pi = 10\pi \text{ radians}$ $\text{Angular speed} = \frac{10\pi}{1200} = \frac{\pi}{120} \text{ radians/second}$

Position Calculation

Brad's position can be modeled using parametric equations based on the angle of rotation $\theta$:

• Vertical position (height): $y(t) = 2.44 + 15(1 - \cos(\theta(t)))$
• Horizontal position: (not necessary for this problem, but can be given by) $x(t) = 15\sin(\theta(t))$

Time Calculation for Points

To find the positions at points B and E:

1. For B and E:
   • Convert the minutes into seconds for calculations.
   • Calculate the angle at each time by using: $\theta(t) = \frac{\pi}{120} t$
   • Plug $t$ values into the $y(t)$ equation to find the height at those times.

For B:

• At $t = 1$ minute = 60 seconds: $\theta(60) = \frac{\pi}{120} \times 60 = \frac{\pi}{2}$ $y(60) = 2.44 + 15(1 - \cos(\frac{\pi}{2})) = 2.44 + 15(1 - 0) = 17.44 \text{ meters}$

• At $t = 4$ minutes = 240 seconds: $\theta(240) = \frac{\pi}{120} \times 240 = 2\pi$ $y(240) = 2.44 + 15(1 - \cos(2\pi)) = 2.44 + 15(1 - 1) = 2.44 \text{ meters}$

For E:

• At $t = 16$ minutes = 960 seconds: $\theta(960) = \frac{\pi}{120} \times 960 = 8\pi$ $y(960) = 2.44 + 15(1 - \cos(8\pi)) = 2.44 + 15(1 - 1) = 2.44 \text{ meters}$

Final Positions

• For B:

  • At $t = 1$: (not matching options)
  • At $t = 4$: (2.44 meters)

• For E:

  • At $t = 4$: (2.44 meters)
  • At $t = 16$: (2.44 meters)

Conclusion

Brad's positions at the specified times do not match the given options directly based on the calculations. We need to check the rounding or other context-based adjustments.

If you want further clarification or additional calculations, please let me know! Here are some related questions to consider:

1. How does the height of the Ferris wheel affect the calculation?
2. What would the positions be if the wheel spun counterclockwise?
3. How can you represent the positions on a graph?
4. What adjustments would you make for a different diameter?
5. How does the angular speed influence the overall experience of the ride?

Tip: Always double-check calculations to ensure accuracy, especially in applications involving periodic functions.