### Rocket Launch Acceleration AnalysisA rocket will carry a communications satellite into low Earth orbit. Suppose that the thrust during the first 200 seconds of flight is provided by solid rocket boosters at different points during liftoff. The graph below shows the acceleration in G-forces (that is, acceleration in \(9.8 \, \text{m/s}^2\) increments) versus time after launch.#### Graph Explanation: Acceleration in G-Forces vs. Time After Liftoff- **Axes:** - **X-Axis (Elapsed Time in seconds):** Ranges from 0 to 200 seconds. - **Y-Axis (Acceleration in G-Forces):** Ranges from 0 to 3 G-forces.- **Data Points:** - At \(t = 15\) seconds, the acceleration is approximately 1.27 G-forces. - At \(t = 65\) seconds, the acceleration is approximately 0.98 G-forces. - At \(t = 186\) seconds, the acceleration is approximately 2.79 G-forces.- **Graph Description:** - The graph is a series of plotted points showing the progression of acceleration over time. Initially, acceleration decreases slightly, and after a certain point (around 65 seconds), it begins to increase, peaking around 186 seconds.#### Questiona. Approximate the interval(s) over which the acceleration is increasing. Write your answer as an interval. Separate multiple intervals with commas, if necessary.The acceleration is increasing over _________________. a. Approximate the interval(s) over which the acceleration is increasing. Write your answer as an interval. Separate multiple intervals with commas, if necessary.The acceleration is increasing over ________________.b. Approximate the interval(s) over which the acceleration is decreasing. Write your answer as an interval. Separate multiple intervals with commas, if necessary.The acceleration is decreasing over ________________.

Solution: a) Looking at the curve the acceleration increases, then decreases, and then increases again. So, the intervals in which the acceleration is increasing are (0,15) and (65,186) So interval is (0,15)∪(65,186) b) So, the intervals in which the acceleration is decreasing are (15,65) and (186,200) So, the interval is (15,65) ∪ (186,200)

Math

Calculus

A rocket will carry a communications satellite into low Earth orbit. Suppose that the thrust during the first 200 sec of flight is provided by solid rocket boosters at different points during liftoff. The graph shows the acceleration in G-forces (that is, acceleration in 9.8 m/sec2 increments) versus time after launch. Acceleration in G-Forces vs. Time After Liftoff (186, 2.79) (15, 1.27)] 1.5 (65,0.98) 0.5 40 80 120 160 200 Elapsed Time (sec) a. Approximate the interval(s) over which the acceleration is increasing. Write your answer as an interval. Separate multiple intervals with commas, if necessary. The acceleration is increasing over. Acceleration (G-Forces)

A rocket will carry a communications satellite into low Earth orbit. Suppose that the thrust during the first 200 sec of flight is provided by solid rocket boosters at different points during liftoff. The graph shows the acceleration in G-forces (that is, acceleration in 9.8 m/sec2 increments) versus time after launch. Acceleration in G-Forces vs. Time After Liftoff (186, 2.79) (15, 1.27)] 1.5 (65,0.98) 0.5 40 80 120 160 200 Elapsed Time (sec) a. Approximate the interval(s) over which the acceleration is increasing. Write your answer as an interval. Separate multiple intervals with commas, if necessary. The acceleration is increasing over. Acceleration (G-Forces)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 44E

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Question

### Rocket Launch Acceleration Analysis

A rocket will carry a communications satellite into low Earth orbit. Suppose that the thrust during the first 200 seconds of flight is provided by solid rocket boosters at different points during liftoff. The graph below shows the acceleration in G-forces (that is, acceleration in \(9.8 \, \text{m/s}^2\) increments) versus time after launch.

#### Graph Explanation: Acceleration in G-Forces vs. Time After Liftoff

- **Axes:**
- **X-Axis (Elapsed Time in seconds):** Ranges from 0 to 200 seconds.
- **Y-Axis (Acceleration in G-Forces):** Ranges from 0 to 3 G-forces.

- **Data Points:**
- At \(t = 15\) seconds, the acceleration is approximately 1.27 G-forces.
- At \(t = 65\) seconds, the acceleration is approximately 0.98 G-forces.
- At \(t = 186\) seconds, the acceleration is approximately 2.79 G-forces.

- **Graph Description:**
- The graph is a series of plotted points showing the progression of acceleration over time. Initially, acceleration decreases slightly, and after a certain point (around 65 seconds), it begins to increase, peaking around 186 seconds.

#### Question

a. Approximate the interval(s) over which the acceleration is increasing. Write your answer as an interval. Separate multiple intervals with commas, if necessary.

The acceleration is increasing over _________________.

a. Approximate the interval(s) over which the acceleration is increasing. Write your answer as an interval. Separate multiple intervals with commas, if necessary.

The acceleration is increasing over ________________.

b. Approximate the interval(s) over which the acceleration is decreasing. Write your answer as an interval. Separate multiple intervals with commas, if necessary.

The acceleration is decreasing over ________________.

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