Could you please help figure out part a for david’s position??Thank you very much Leigh and David are playing a game of laser tag'. David has managed to climb aboard a mining carttravelling along a parabolic track, while Leigh has been caught exposed trying to walk along a narrowpath on the edge of a cliff. As long as David is in the cart he can only fire his laser at right angles tothe direction of motion. If Leigh is caught in David's sight line he is doomed, but he can see a gapbetween the cliff and some rocks ahead of him. If he can get far enough into the gap David will notbe able to see him and tag him. A rough schematic of the situation is sketched below.Cart TracksDavidDirection of FireRocksLeighSafetyCliff EdgeThis situation can be modelled on the cartesian plane as follows, where all quantities are measured inSI units:• Let s e [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, witha positive constant speed v.• David's position is represented by a point that travels along the parabola y =x² – 6x + 14 so• that at time s the x-coordinate is s.ser 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 ofwhichpasses through David'sS,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 Davidwithout being tagged? Justify your answer.(e) Use DESMOS to draw a graph with all the features of this model. Your drawing needs to beable to represent variable values of time and include labels (not hand-written) for every feature.Include a screenshot of this graph with a viewing window x E [-2, 20] and yE[-2,15] in yoursolution.(f) Calculate the minimum speed that Leigh needs to travel at in order to escape. Justify youranswer. (Hint: Think about the value of s where David's line of fire hits the bottom of the rocks.)

(a) Leigh travels along the xAxis with the velocity v at the time s. We know that,…

Leigh and David are playing a game of laser tagʻ. 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.

Leigh and David are playing a game of laser tagʻ. 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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

Question

Could you please help figure out part a for david’s position??Thank you very much

Leigh and David are playing a game of laser tag'. 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.
Cart Tracks
David
Direction of Fire
Rocks
Leigh
Safety
Cliff Edge
This situation can be modelled on the cartesian plane as follows, where all quantities are measured in
SI units:
• Let s e [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 time s the x-coordinate is s.
ser 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
which
passes through David's
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.
(e) Use DESMOS to draw a graph with all the features of this model. Your drawing needs to be
able to represent variable values of time and include labels (not hand-written) for every feature.
Include a screenshot of this graph with a viewing window x E [-2, 20] and yE[-2,15] in your
solution.
(f) Calculate the minimum speed that Leigh needs to travel at in order to escape. Justify your
answer. (Hint: Think about the value of s where David's line of fire hits the bottom of the rocks.)

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