suppose the tourist in question 1 instead threw the rock with the initial velocity of 8.0 m/s [down]. Determine the velocity and displacement of the rock at 4.0 seconds. (remember the vi is down and must become a -8.0 m/s)

To solve for the **velocity** and **displacement** of the rock at 4.0 seconds, we will use the following kinematic equations:

1. **Velocity** equation:
\[
v_f = v_i + a \cdot t
\]
Where:
- \( v_f \) = final velocity
- \( v_i = -8.0 \, \text{m/s} \) (the negative sign indicates downward direction)
- \( a = g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity, also in the downward direction)
- \( t = 4.0 \, \text{seconds} \)

2. **Displacement** equation:
\[
d = v_i \cdot t + \frac{1}{2} a \cdot t^2
\]
Where:
- \( d \) = displacement
- \( v_i = -8.0 \, \text{m/s} \)
- \( a = 9.8 \, \text{m/s}^2 \)
- \( t = 4.0 \, \text{seconds} \)

### Step 1: Finding the final velocity
Substitute the values into the velocity equation:
\[
v_f = -8.0 \, \text{m/s} + (9.8 \, \text{m/s}^2 \cdot 4.0 \, \text{seconds})
\]
\[
v_f = -8.0 \, \text{m/s} + 39.2 \, \text{m/s} = 31.2 \, \text{m/s}
\]
So, the final velocity after 4 seconds is **31.2 m/s [down]**.

### Step 2: Finding the displacement
Now, using the displacement equation:
\[
d = (-8.0 \, \text{m/s}) \cdot 4.0 \, \text{seconds} + \frac{1}{2} (9.8 \, \text{m/s}^2) \cdot (4.0 \, \text{seconds})^2
\]
\[
d = -32.0 \, \text{m} + \frac{1}{2} \cdot 9.8 \, \text{m/s}^2 \cdot 16.0 \, \text{seconds}^2
\]
\[
d = -32.0 \, \text{m} + 78.4 \, \text{m}
\]
\[
d = 46.4 \, \text{m}
\]
So, the displacement after 4 seconds is **46.4 meters [down]**.

### Final Answer:
- **Final velocity**: 31.2 m/s [down]
- **Displacement**: 46.4 m [down]

Would you like more details on any step, or help with another problem?

Here are five related questions to deepen your understanding:
1. What would the final velocity be if the initial velocity was zero?
2. How would the displacement change if the rock was thrown upward with 8.0 m/s?
3. What happens to the displacement if the time was reduced to 2 seconds?
4. How does the direction of velocity affect the motion equations?
5. What would be the time taken for the rock to hit the ground if thrown from 100 meters?

**Tip:** Always ensure that signs in kinematic equations match the direction of motion. This helps avoid confusion and incorrect answers.

Suppose the tourist in question 1 instead threw the rock with the initial velocity of 8.0 m/s [down]. Determine the velocity and displacement of the rock at 4.0 seconds. (Remember the vi is down and must become a -8.0 m/s).

Learn how to calculate the velocity and displacement of a rock thrown downward with an initial velocity of 8.0 m/s after 4 seconds. Using kinematic equations, this step-by-step guide demonstrates the calculations for high school physics students. Suitable for Grades 9-12.

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