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The function defined by d = 50 + 3121 – 16r gives the height in feet of a cannonball / seconds after the ball leaves the cannon. 1. What do the terms 50, 3121, and -16r tell us about the cannonball? 2. Use graphing technology to graph the function. Adjust the graphing window to the following boundaries: 0

The function defined by d = 50 + 3121 – 16r gives the height in feet of a cannonball / seconds after the ball leaves the cannon. 1. What do the terms 50, 3121, and -16r tell us about the cannonball? 2. Use graphing technology to graph the function. Adjust the graphing window to the following boundaries: 0

Algebra and Trigonometry (6th Edition)
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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## Understanding the Cannonball Trajectory The function defined by \( d = 50 + 312t - 16t^2 \) gives the height in feet of a cannonball \( t \) seconds after the ball leaves the cannon. ### Exploration Questions: 1. **Analyzing the Function Terms** What do the terms 50, 312t, and \(-16t^2\) tell us about the cannonball? 2. **Graphing the Function** Use graphing technology to graph the function. Adjust the graphing window to the following boundaries: \( 0 < x < 25 \) and \( 0 < y < 2,000 \). 3. **Graph Analysis** - **a. Describe the shape of the graph.** What does it tell us about the movement of the cannonball? - **b. Estimate the maximum height the ball reaches.** When does this happen? - **c. Estimate when the ball hits the ground.** ### Diagram Explanation The graph of the function should display a parabolic curve, indicating the vertical motion of the cannonball as it rises to a peak (maximum height) before descending back to the ground. The initial upward movement is demonstrated by the positive linear term \( 312t \), while the downward, concave shape of the parabola is determined by the negative quadratic term \(-16t^2\). Adjusting the graphing window ensures that the observation focuses on the relevant section of the trajectory.
Transcribed Image Text:## Understanding the Cannonball Trajectory The function defined by \( d = 50 + 312t - 16t^2 \) gives the height in feet of a cannonball \( t \) seconds after the ball leaves the cannon. ### Exploration Questions: 1. **Analyzing the Function Terms** What do the terms 50, 312t, and \(-16t^2\) tell us about the cannonball? 2. **Graphing the Function** Use graphing technology to graph the function. Adjust the graphing window to the following boundaries: \( 0 < x < 25 \) and \( 0 < y < 2,000 \). 3. **Graph Analysis** - **a. Describe the shape of the graph.** What does it tell us about the movement of the cannonball? - **b. Estimate the maximum height the ball reaches.** When does this happen? - **c. Estimate when the ball hits the ground.** ### Diagram Explanation The graph of the function should display a parabolic curve, indicating the vertical motion of the cannonball as it rises to a peak (maximum height) before descending back to the ground. The initial upward movement is demonstrated by the positive linear term \( 312t \), while the downward, concave shape of the parabola is determined by the negative quadratic term \(-16t^2\). Adjusting the graphing window ensures that the observation focuses on the relevant section of the trajectory.
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