Divide up into groups of at least 2 and no more than 4. Turn in on sheet per gro
ID: 3111122 • Letter: D
Question
Divide up into groups of at least 2 and no more than 4. Turn in on sheet per group. The hunt for Red October is on! (Remember the 1990 Sean Connery - Alec Baldwin movie?) Two surface ships, the HMS Repulse and the USS Bedford maneuver to try to determine the submarine's course and speed. With the information a P - 3 Orion antisubmarine aircraft can prepare to intercept the Red October. The Repulse is located at (4, 0, 0) whereas the Bedford is located at (0, 5, 0) All Coordinates are given in thousands of feet. The sonar from the Repulse locates the submarine in the direction of the vector i + (3/2)j - (1/4)k, and the Bedford locates Red October in direction of the vector 2I - (2/3) - (1/6)k. Four minutes ago the submarine was located at (2, - 7, - 1/2). The Orion flies at an elevation 1,000 feet and is due in 20 minutes. Assuming that Red October moves in a straight line at a constant speed, to what coordinates should the surface ships direct the aircraft? Do not "sink the plane. How fast is Red October travelling in knots (nautical miles per hour, 1 nautical mile is 6, 076 feet)? At what depth should the crew of the Orion set the "ball and chain? " The "ball and chain" is a device that attaches to the hull on a submarine and "ball and deploys a steel ball attached to a chain. As the submarine travels, the ball bangs against the hull, forcing the submarine to surface. [Quote from the movie: "The art of playing chicken is knowing when to flinch."]Explanation / Answer
unit = thousand feet
repulse (4,0,0) vector = i+(3/2)j-(1/4)k.. so any point on the that line can be wriiten as
(x,y,z)=(4+t , (3/2)t , -(t/4) ) ----->1
bedford (0,5,0) vector = 2i-(2/3)j-(1/6)k...so any point on the that line can be wriiten as
(x,y,z) = (2u , 5 - (2/3)u , -(1/6)u ) -----> 2
1 and 2 are same and sub marine is currently located there
-(t/4)= -(1/6)u...so t=(2/3)u
4+t=2u
4+(2/3)u=2u
4=(4/3)u....u=3...t=2...
currently submarine is located at (6,3, -1/2)
4 minutes ago it was at (2, -7, -1/2)...
direction in which it is moving is... (6-2) i + 3-(-7)j + (-1/2 - (-1/2)k = 4i+10j
so in 1 minute the submarine is moving 1 unit in +x and 1 unit in +y direction
so after 20 minutes the submarine the submarines position will be
(6+20,3+20, -1/2) = (26 , 23 , -1/2)
the orion flies at an elevation of 1000 ft.. i.e 1unit
for orion to attack submarines.. it shud be above the submarine.. so the ships shud direct it at the coordinates
(26, 23 , 1)... z axis is the depth