https://file.aiquickdraw.com/mathbot/file/173033812791624ldpxpq.jpg

Let's go through each part of the problem.

### Part (a)
We are asked to find the maximum height (y) Chris reaches. Given:
- Initial velocity (\( v_0 \)) = 3.724 m/s
- Time to reach the highest point (\( t \)) = 0.38 s
- At the highest point, final velocity (\( v_f \)) = 0 m/s
- Acceleration due to gravity (\( a \)) = -9.81 m/s² (acting downward)

Using the kinematic formula:
\[
y = v_0 t + \frac{1}{2} a t^2
\]

Plugging in the values:
\[
y = (3.724 \, \text{m/s})(0.38 \, \text{s}) + \frac{1}{2} (-9.81 \, \text{m/s}^2)(0.38 \, \text{s})^2
\]

### Part (b)
To find Chris's total hang time, we double the time it takes to reach the highest point, since the time to go up is the same as the time to come down:
\[
\text{Total time} = 2 \times 0.38 \, \text{s} = 0.76 \, \text{s}
\]

### Part (c)
The basketball hoop is 3.05 m high. Chris can reach 2.29 m with his arms up. We need to see if his jump height from part (a) adds enough to reach 3.05 m.

### Part (d)
On Doucettune, Chris jumps with the same initial velocity, reaching a height of 5.48 m. We need to calculate the gravitational acceleration on Doucettune using the kinematic equation rearranged for \( a \):
\[
y = \frac{v_0^2}{2a}
\]
where \( y = 5.48 - 2.29 \) meters.

Would you like further calculation steps or explanations on any part?

---

1. How would you solve for final velocity in other kinematic equations?
2. What other kinematic formulas could help solve these types of problems?
3. Why is time doubled in part (b)?
4. How does gravitational acceleration affect jump height?
5. What assumptions are made about gravity on Doucettune?

**Tip:** Always double-check unit consistency to avoid errors.

Chris wants to dunk a basketball. Solve for his jump height, hang time, and whether he can dunk. Also, calculate the gravitational acceleration on another planet based on a similar jump.

Explore a challenging physics problem involving kinematic equations to determine jump height, hang time, and gravitational acceleration on another planet. Ideal for high school students learning about free fall and gravity.

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