Use false position method to determine the drag coefficient needed so that a 95-kg bungee jumper has a velocity of 46 m/s after 9 s of free fall. Start with initial guesses of x=0.2 and xu-0.5 and iterate until the approximate relative error fails below 5%. Note: The acceleration of gravity is 9.81 m/s2 (Round the final answer to four decimal places) The required drag coefficient is co kg/m.

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### Determining the Drag Coefficient for a Bungee Jumper

Use the false-position method to determine the drag coefficient needed so that a 95-kg bungee jumper has a velocity of 46 m/s after 9 s of free fall. Start with initial guesses of \( x_l = 0.2 \) and \( x_u = 0.5 \) and iterate until the approximate relative error falls below 5%.

**Note:** The acceleration of gravity is 9.81 m/s². (Round the final answer to four decimal places.)

The required drag coefficient is \( c_D = \_\_\_\_\_ \) kg/m.

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For further clarification:
- **False-position method:** An iterative numerical method for finding roots of a function, effectively used for solving equations.
- **Variables \( x_l \) and \( x_u \):** Represent the lower and upper bounds for the initial guesses of the drag coefficient.
- **Relative error:** The measure of error between iterations, which should fall below 5% for satisfactory accuracy.

This problem involves applying principles of physics and numerical methods to solve for the drag coefficient that ensures the specified conditions for the bungee jumper's motion are met.
Transcribed Image Text:### Determining the Drag Coefficient for a Bungee Jumper Use the false-position method to determine the drag coefficient needed so that a 95-kg bungee jumper has a velocity of 46 m/s after 9 s of free fall. Start with initial guesses of \( x_l = 0.2 \) and \( x_u = 0.5 \) and iterate until the approximate relative error falls below 5%. **Note:** The acceleration of gravity is 9.81 m/s². (Round the final answer to four decimal places.) The required drag coefficient is \( c_D = \_\_\_\_\_ \) kg/m. --- For further clarification: - **False-position method:** An iterative numerical method for finding roots of a function, effectively used for solving equations. - **Variables \( x_l \) and \( x_u \):** Represent the lower and upper bounds for the initial guesses of the drag coefficient. - **Relative error:** The measure of error between iterations, which should fall below 5% for satisfactory accuracy. This problem involves applying principles of physics and numerical methods to solve for the drag coefficient that ensures the specified conditions for the bungee jumper's motion are met.
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