Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Determine the (x, y) co-ordinates for Leigh's and David's position at time s. which Find the equation of a normal line to the parabola, in terms of s, which passes through David's position. Find the point H where the normal line found in (b) intersects the x-axis in terms of s. If there were no rocks available for Leigh to hide in, would he be able to escape from David without being tagged? Justify your answer.

Determine the (x, y) co-ordinates for Leigh's and David's position at time s. which Find the equation of a normal line to the parabola, in terms of s, which passes through David's position. Find the point H where the normal line found in (b) intersects the x-axis in terms of s. If there were no rocks available for Leigh to hide in, would he be able to escape from David without being tagged? Justify your answer.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

How do I do part (d)?

Leigh and David are playing a game of laser tag¹. David has managed to climb aboard a mining cart travelling along a parabolic track, while Leigh has been caught exposed trying to walk along a narrow path on the edge of a cliff. As long as David is in the cart he can only fire his laser at right angles to the direction of motion. If Leigh is caught in David's sight line he is doomed, but he can see a gap between the cliff and some rocks ahead of him. If he can get far enough into the gap David will not be able to see him and tag him. A rough schematic of the situation is sketched below. David Direction of Fire ● Leigh, Cliff Edge Cart Tracks Rocks X Safety This situation can be modelled on the cartesian plane as follows, where all quantities are measured in SI units: • Let s € [0,00) be a variable representing time. Leigh's position is represented by a point that travels along the x-axis, starting at the origin, with a positive constant speed v. • David's position is represented by a point that travels along the parabola y = x² - 6x + 14 so - that at times the x-coordinate is s. er tag is a game where you try to shoot (tag) your opponent using a low-powered laser
Transcribed Image Text:Leigh and David are playing a game of laser tag¹. David has managed to climb aboard a mining cart travelling along a parabolic track, while Leigh has been caught exposed trying to walk along a narrow path on the edge of a cliff. As long as David is in the cart he can only fire his laser at right angles to the direction of motion. If Leigh is caught in David's sight line he is doomed, but he can see a gap between the cliff and some rocks ahead of him. If he can get far enough into the gap David will not be able to see him and tag him. A rough schematic of the situation is sketched below. David Direction of Fire ● Leigh, Cliff Edge Cart Tracks Rocks X Safety This situation can be modelled on the cartesian plane as follows, where all quantities are measured in SI units: • Let s € [0,00) be a variable representing time. Leigh's position is represented by a point that travels along the x-axis, starting at the origin, with a positive constant speed v. • David's position is represented by a point that travels along the parabola y = x² - 6x + 14 so - that at times the x-coordinate is s. er tag is a game where you try to shoot (tag) your opponent using a low-powered laser
•The rocks are represented by a the line segment x = 10 for y ≥ 3. (a) Determine the (x, y) co-ordinates for Leigh's and David's position at time s. (b) Find the equation of a normal line to the parabola, in terms of s, which passes through David's position. (c) Find the point H where the normal line found in (b) intersects the x-axis in terms of s. (d) If there were no rocks available for Leigh to hide in, would he be able to escape from David without being tagged? Justify your answer.
Transcribed Image Text:•The rocks are represented by a the line segment x = 10 for y ≥ 3. (a) Determine the (x, y) co-ordinates for Leigh's and David's position at time s. (b) Find the equation of a normal line to the parabola, in terms of s, which passes through David's position. (c) Find the point H where the normal line found in (b) intersects the x-axis in terms of s. (d) If there were no rocks available for Leigh to hide in, would he be able to escape from David without being tagged? Justify your answer.
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS