https://file.aiquickdraw.com/mathbot/file/1727497028634fti000dl.jpg

The image contains a quadratic function assignment that focuses on the motion of a rocket. The height of the rocket \( h(t) \) above sea level as a function of time \( t \) is given by the equation:

\[
h(t) = -4.9t^2 + 361t + 108
\]

There are two main parts to the question:

1. **Time of Splashdown**: The rocket splashes into the ocean at \( t = 73.9 \) seconds.
2. **Maximum Height**: The rocket reaches its peak height of \( 6640.78 \) meters.

Let me know if you'd like to explore how the peak height and time of splashdown were calculated, or if you'd like help with another specific part of the problem!

### Here are 5 follow-up questions to think about:
1. How is the formula for the height of the rocket derived?
2. Why is there a negative coefficient for the \( t^2 \)-term in the height equation?
3. How can we calculate the time at which the rocket reaches its peak height?
4. How would the equation change if the rocket's initial velocity or height were different?
5. What would happen to the height-time graph if the gravity value (currently 4.9 m/s²) was different?

### Tip:
When solving quadratic equations like this, the peak (or vertex) of the parabola can be found using the formula \( t = \frac{-b}{2a} \), where the quadratic is in the form \( at^2 + bt + c \).

NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t) = -4.9t^2 + 361t + 108. Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? How high above sea-level does the rocket get at its peak?

Learn how to solve a quadratic function related to the height of a NASA rocket over time. Discover the peak height of the rocket and the exact time it splashes down into the ocean using the quadratic equation: h(t) = -4.9t^2 + 361t + 108. Ideal for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation