Please solve Q.e only into detail (Some of my friends derivative H twice to get the acceleration of H and compare with the acceleration of Leigh to solve this question. Is it right? If it is right, can you solve this question in that way too beside your method? Thank you.)
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.
Safety
This situation can be modelled on the cartesian plane as follows,where all quantities are measured in SI units: Let s e[0be 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=x-6x+14 so that at time s the x-coordinate is s The rocks are represented by a line segment x=10 for y3
(a) Determine thex,y coordinates 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. 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 [2,20] and y [-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.
