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) = -4.9t² +64t+353. Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? The rocket splashes down after How high above sea-level does the rocket get at its peak? The rocket peaks at seconds. meters above sea-level.
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) = -4.9t² +64t+353. Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? The rocket splashes down after How high above sea-level does the rocket get at its peak? The rocket peaks at seconds. meters above sea-level.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Rocket Launch Analysis**
NASA launches a rocket at \( t = 0 \) seconds. Its height, in meters above sea level, as a function of time is given by \( h(t) = -4.9t^2 + 64t + 353 \).
**Question 1: Splashdown Time**
Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
The rocket splashes down after \[ _____ \] seconds.
**Question 2: Peak Height**
How high above sea level does the rocket get at its peak?
The rocket peaks at \[ _____ \] meters above sea level.
**Graph/Diagram Explanation**
While there is no specific graph or diagram provided in the text, we can descriptively explain the height function with respect to time. The function \( h(t) = -4.9t^2 + 64t + 353 \) represents a parabolic trajectory of the rocket. The coefficient \( -4.9 \) indicates the downward acceleration due to gravity, whereas \( 64t \) represents the initial upward velocity component, and \( 353 \) is the launch height in meters above sea level.
For educational purposes, the trajectory can be visualized as a quadratic graph where:
- The peak of the parabola represents the highest point the rocket reaches.
- The roots of the function (where \( h(t) = 0 \)) would represent the time when the rocket hits the sea level, indicating splashdown.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f8a397f-4115-4363-8e32-37a2c2950f08%2F587d911f-1dd8-4de1-a19a-c5facfa754f6%2Fm68u1pl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Rocket Launch Analysis**
NASA launches a rocket at \( t = 0 \) seconds. Its height, in meters above sea level, as a function of time is given by \( h(t) = -4.9t^2 + 64t + 353 \).
**Question 1: Splashdown Time**
Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
The rocket splashes down after \[ _____ \] seconds.
**Question 2: Peak Height**
How high above sea level does the rocket get at its peak?
The rocket peaks at \[ _____ \] meters above sea level.
**Graph/Diagram Explanation**
While there is no specific graph or diagram provided in the text, we can descriptively explain the height function with respect to time. The function \( h(t) = -4.9t^2 + 64t + 353 \) represents a parabolic trajectory of the rocket. The coefficient \( -4.9 \) indicates the downward acceleration due to gravity, whereas \( 64t \) represents the initial upward velocity component, and \( 353 \) is the launch height in meters above sea level.
For educational purposes, the trajectory can be visualized as a quadratic graph where:
- The peak of the parabola represents the highest point the rocket reaches.
- The roots of the function (where \( h(t) = 0 \)) would represent the time when the rocket hits the sea level, indicating splashdown.
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