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To solve this problem, we need to calculate the time it takes for a toy rocket to reach its highest point when launched with an initial speed of 45.0 m/s. Here’s the solution:

### Solution
1. **Given Data**:
   - Initial velocity (\( v_0 \)) = 45.0 m/s (upwards).
   - Final velocity at the highest point (\( v \)) = 0 m/s (since the rocket stops momentarily at the highest point).
   - Acceleration (\( a \)) = \( -9.8 \, \text{m/s}^2 \) (the acceleration due to gravity, acting downward).

2. **Using the Equation of Motion**:
   To find the time taken to reach the highest point, we can use the formula:
   \[
   v = v_0 + at
   \]
   Rearranging to solve for \( t \):
   \[
   t = \frac{v - v_0}{a}
   \]

3. **Substitute the Known Values**:
   \[
   t = \frac{0 - 45.0}{-9.8} = \frac{-45.0}{-9.8} = 9.17 \, \text{seconds}
   \]

### Answer
The time it takes for the rocket to reach its highest point is **9.17 seconds**.

Would you like further explanation on any part of this solution?

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Here are some related questions you might explore:
1. What is the maximum height the rocket reaches?
2. How long will it take for the rocket to return to the ground?
3. What would the final velocity of the rocket be just before it hits the ground?
4. How would the time change if the rocket were launched with a different initial speed?
5. What factors affect the rocket’s time to reach its highest point?

**Tip:** In free-fall problems, always keep in mind the direction of acceleration due to gravity, which is typically \( -9.8 \, \text{m/s}^2 \) on Earth.

A toy rocket is shot straight up into the air with an initial speed of 45.0 m/s. How long does it take for the rocket to reach its highest point?

Learn how to calculate the time it takes for a toy rocket launched at 45.0 m/s to reach its highest point. This problem demonstrates key kinematic principles and involves applying the velocity equation for projectile motion, suitable for students in Grades 9-12.

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