You throw a small rock straight up from the edge of a high way bridge that crosses a river. The rock passes you on it's way down, 6.00s after it was thrown. What is the speed of the rock just before it reaches the water 28.0m below the point where the rock left your hand? Ignore air resistance

To solve this problem, we can use the principles of kinematics. Here’s how we can approach it:

### Step 1: Analyze the given information
- Time \( t = 6.00 \) seconds (the total time the rock takes to pass the same point from where it was thrown).
- Distance from the point of throw to the water \( h = 28.0 \) meters.
- Acceleration due to gravity \( g = 9.81 \, \text{m/s}^2 \).
- Initial velocity \( v_0 \) is what we need to find first, which is the velocity when the rock is thrown upward.

### Step 2: Use kinematic equations
First, find the initial velocity \( v_0 \) when the rock is thrown. Since the rock passes the point where it was thrown after 6 seconds, we know that it must have taken half of this time (3 seconds) to reach the highest point and another 3 seconds to return to the same level.

#### At the highest point:
- The velocity \( v \) at the highest point is \( 0 \, \text{m/s} \) because the rock momentarily stops before falling back down.

Using the kinematic equation:
\[
v = v_0 - g \cdot t
\]
where \( v = 0 \, \text{m/s} \) at the highest point, and \( t = 3 \, \text{seconds} \),
\[
0 = v_0 - (9.81 \, \text{m/s}^2) \cdot 3 \, \text{seconds}
\]
\[
v_0 = 9.81 \, \text{m/s}^2 \cdot 3 \, \text{seconds}
\]
\[
v_0 = 29.43 \, \text{m/s}
\]

### Step 3: Determine the speed just before hitting the water
Now, we calculate the final velocity \( v_f \) just before the rock hits the water using the following kinematic equation:
\[
v_f^2 = v_0^2 + 2gh
\]
where \( h = 28.0 \, \text{m} \).

Substituting the values:
\[
v_f^2 = 29.43^2 + 2 \cdot 9.81 \cdot 28.0
\]
\[
v_f^2 = 865.3 + 549.36
\]
\[
v_f^2 = 1414.66
\]
\[
v_f = \sqrt{1414.66}
\]
\[
v_f \approx 37.61 \, \text{m/s}
\]

### Final Answer:
The speed of the rock just before it reaches the water is approximately **37.61 m/s**.

Would you like a more detailed breakdown of these steps or have any further questions?

Here are five related questions:
1. How would air resistance affect the speed of the rock before it hits the water?
2. What would happen to the time taken if the height of the bridge was doubled?
3. How would the result change if the rock were thrown at an angle instead of straight up?
4. What is the maximum height the rock reaches above the throw point?
5. How would the initial speed change if the rock took 8 seconds to pass the throw point?

**Tip:** Always ensure to check your units in calculations, as they can drastically affect your final answer!

Learn how to calculate the speed of a rock just before it hits water, thrown from a bridge using principles of kinematics. Includes step-by-step solution with detailed calculations. Suitable for Grades 11-12.

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