Gwyneth is developing a computer game based on the popular game Battleships. The objective of the game is to fire missiles to try to sink each other's ships. The trajectory of a missile after it is fired from a ship is modelled in the computer code by a quadratic equation of the form y = ax? + bx + c, where y represents the height (in centimetres) of the missile above the virtual sea, and x represents the horizontal distance (in centimetres) of the missile from the position where it was launched. The values of a, b and c are determined by the computer code that Gwyneth writes, and depend on the angle and force at which the missile is launched. You may assume that the virtual sea area where the battle takes place is completely flat and horizontal (a) The quadratic equation produced to model the trajectory of a test missile is y = -0.08x2 + 2.15x + 0.38. In this part of the question, you are asked to consider the graph modelled by this quadratic equation. (i) What does the y-intercept represent in the context of this model? (ii) Use the quadratic formula to find the x-intercepts. Give your answers correct to two decimal places
Gwyneth is developing a computer game based on the popular game Battleships. The objective of the game is to fire missiles to try to sink each other's ships. The trajectory of a missile after it is fired from a ship is modelled in the computer code by a quadratic equation of the form y = ax? + bx + c, where y represents the height (in centimetres) of the missile above the virtual sea, and x represents the horizontal distance (in centimetres) of the missile from the position where it was launched. The values of a, b and c are determined by the computer code that Gwyneth writes, and depend on the angle and force at which the missile is launched. You may assume that the virtual sea area where the battle takes place is completely flat and horizontal (a) The quadratic equation produced to model the trajectory of a test missile is y = -0.08x2 + 2.15x + 0.38. In this part of the question, you are asked to consider the graph modelled by this quadratic equation. (i) What does the y-intercept represent in the context of this model? (ii) Use the quadratic formula to find the x-intercepts. Give your answers correct to two decimal places
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
![Gwyneth is developing a computer game based on the popular game
Battleships. The objective of the game is to fire missiles to try to sink each
other's ships. The trajectory of a missile after it is fired from a ship is
modelled in the computer code by a quadratic equation of the form
y =
ax?
+ bx + c,
where y represents the height (in centimetres) of the missile above the
virtual sea, and x represents the horizontal distance (in centimetres) of the
missile from the position where it was launched. The values of a, b and c are
determined by the computer code that Gwyneth writes, and depend on the
angle and force at which the missile is launched. You may assume that the
virtual sea area where the battle takes place is completely flat and horizontal.
(a) The quadratic equation produced to model the trajectory of a test
missile is
y = -0.08x²
+ 2.15x + 0.38.
In this part of the question, you are asked to consider the graph
modelled by this quadratic equation.
(i) What does the y-intercept represent in the context of this model?
(ii) Use the quadratic formula to find the x-intercepts. Give your
answers correct to two decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb7e6b7d-87ae-45bb-ba78-dbd65b71c2ad%2F6e1fafe0-c8a6-498a-9eca-07b321a9584c%2F71nxb9_processed.png&w=3840&q=75)
Transcribed Image Text:Gwyneth is developing a computer game based on the popular game
Battleships. The objective of the game is to fire missiles to try to sink each
other's ships. The trajectory of a missile after it is fired from a ship is
modelled in the computer code by a quadratic equation of the form
y =
ax?
+ bx + c,
where y represents the height (in centimetres) of the missile above the
virtual sea, and x represents the horizontal distance (in centimetres) of the
missile from the position where it was launched. The values of a, b and c are
determined by the computer code that Gwyneth writes, and depend on the
angle and force at which the missile is launched. You may assume that the
virtual sea area where the battle takes place is completely flat and horizontal.
(a) The quadratic equation produced to model the trajectory of a test
missile is
y = -0.08x²
+ 2.15x + 0.38.
In this part of the question, you are asked to consider the graph
modelled by this quadratic equation.
(i) What does the y-intercept represent in the context of this model?
(ii) Use the quadratic formula to find the x-intercepts. Give your
answers correct to two decimal places.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 1 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)