https://file.aiquickdraw.com/mathbot/file/1730338034578jclf9k5l.jpg

Let's go through each part of the problem step-by-step and verify the calculations.

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### Problem 20: Chris wants to dunk a basketball.

#### Part (a) - Calculating Jump Height
- **Given values**:
  - \( v_0 = 3.724 \, \text{m/s} \) (initial velocity)
  - \( v_f = 0 \, \text{m/s} \) (velocity at the highest point)
  - \( a = -9.8 \, \text{m/s}^2 \) (acceleration due to gravity)
  - \( t = 0.38 \, \text{s} \) (time to reach the highest point)
  
- **Formula**: We use the kinematic equation:
  \[
  y = \frac{v_f^2 - v_0^2}{2a}
  \]

- **Calculation**:
  \[
  y = \frac{0^2 - (3.724)^2}{2 \times (-9.8)} = \frac{-13.864}{-19.6} = 0.708 \, \text{m}
  \]
  
Chris jumps **0.708 meters** high.

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#### Part (b) - Calculating Total Hang Time
- **Explanation**: The time to reach the highest point is \( 0.38 \, \text{s} \). Since the motion is symmetric, the total time (up and down) is:
  \[
  \text{Total time} = 0.38 \times 2 = 0.76 \, \text{s}
  \]
  
Chris's total hang time is **0.76 seconds**.

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#### Part (c) - Can Chris Dunk?
- **Given**: 
  - The basketball hoop height is \( 3.05 \, \text{m} \).
  - Chris's reach with his arms extended is \( 2.29 \, \text{m} \).
  
- **Calculation**:
  \[
  \text{Max height Chris can reach} = 2.29 + 0.708 = 2.998 \, \text{m}
  \]
  
Since **2.998 m < 3.05 m**, Chris **cannot dunk**.

---

#### Part (d) - Calculating Gravity on Planet Doucettene
- **Given values**:
  - \( y = 3.19 \, \text{m} \) (height Chris reached on Doucettene)
  - \( v_0 = 3.724 \, \text{m/s} \)
  - \( v_f = 0 \, \text{m/s} \)
  
- **Formula**: We rearrange the same kinematic equation used in part (a):
  \[
  a = \frac{v_f^2 - v_0^2}{2y}
  \]

- **Calculation**:
  \[
  a = \frac{0^2 - (3.724)^2}{2 \times 3.19} = \frac{-13.864}{6.38} = -2.17 \, \text{m/s}^2
  \]
  
The acceleration due to gravity on Doucettene is **-2.17 m/s²**.

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Would you like a breakdown of any part of these solutions? 

Here are some follow-up questions you might find helpful:

1. Why is gravity's value negative in the equations?
2. What would Chris's jump height be if he jumped with a different initial velocity?
3. How would Doucettene’s lower gravity affect Chris’s hang time?
4. Could Chris achieve the necessary height with a slight increase in jump speed on Earth?
5. Why do we assume that air resistance is negligible in these calculations?

**Tip**: Always double-check unit consistency across equations, as it helps prevent errors.

Chris wants to dunk a basketball.

A video shows it takes Chris 0.38s to jump to his highest point when he jumps with an initial velocity of 3.724 m/s. How high did Chris jump?

What was Chris’s total hang time in the air?

A basketball hoop is 3.05m. Standing with arms up he can reach 2.29m. If he jumps exactly like he did in part a, can Chris dunk?

Chris goes to the planet Doucettene. He jumps with the same initial velocity but this time he jumps up as high as he can and touches a tree branch that is 5.48m high off the ground. What is the acceleration of gravity on this planet?

Explore how to calculate Chris's jump height, total hang time, and ability to dunk a basketball with given initial velocity and gravitational acceleration. This problem also examines planetary gravity through Chris's jump on planet Doucettene. Ideal for Grades 10-12, covering kinematics and gravity.

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