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.)

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 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.)

Accepted Answer

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