Question

Can anyone pls help, a,b,c (i,ii,iii)? Thank You

1 Cat and Mouse [5 marks] You and a friend both purchase dune buggies. These off-road vehicles are excellent for driving on sand. To test out your new rides, you decide to play a game of cat and mouse in a desert with sand dunes Both of you start in the same location. You give your friend a head start, then attempt to catch up to them. To give you a chance, they radio you their coordinates several times. You may assume that both dune buggies start at the origin (0,0,0), and that each coordinate contains an East-West component, a North-South component and a height component, relative to the origin. Let positive movement in the i direction be East, positive movement in the j direction be North, and positive movement in the k direction correspond to increasing height Your friend radios you the following four coordinates in order: O (0,0,0) P (250,400, 30) Po: (800, 500, 20) Ps (1000,800, 40) Note that the first transmission is the origin, just to test that your radios are working! (a) Determine the displacement vectors describing your friends trajectory between each of their trans- missions 1 mark] (b) Determine the magnitude of the displacement of Ps from the origin [1 mark] (c) Suppose that when you receive the transmission corresponding to P2, you are located at a point Y with coordinates Y(500, 600). For this part, you may neglect the height component of all points, and consider the problem in terms of 2-dimensional vectors (East-West and North-South) (i) Determine the angle, θ, between your effective straight-line trajectory to the point Y and your friends effective straight-line trajectory to the point P2 [1 mark] (ii) Suppose that you now travel from Y, parallel to P2P3, such that if you were to continue on this tra- jectory without changing direction, you would eventually reach the point (1100,1500). Draw a schematic (without specific values) showing at least the points Y, P3, your trajectory, and the point P on your trajectory that is closest to P3 [1 mark] Hint: The shortest distance between a point and a lin e is on a path perpendicular to the line (iii) Show that the closest that you get to the point Ps along this trajectory is (approximately) the point (746,969). 1 mark]

Answer 1

Solution Page No-O ven o uu P:250, uoo, 30 ( 800, 500, 20 כ : 3'.C lo00, goo ,ub). o) oetermine the displacement vechos descobing trangmiss on C20 -30)k

b) nognitud e of the dlis placement Poem the 164160 0 r3 1281.25 P neglecg heiht cempo nent : 800, 500 . anol Pos tion of mine, y (500, 600) when foiEnd So effective stoaight n raecbomy h me

toP) 5o0 x 55600 x100 2450 + 60 o Co8θ ヌ673 7.01 x5.59 y-50 S0o-600(x-800) 000-8 2-

saisfies the Point (rooo will be aith satisP'ves ļueron of 69.23.

so Point P.(籼6-15,969,23) її, poem obove Point P (Xu6. 15,969.23)