In: Physics
The hunt for Red October is on! (Remember the 1990 Sean Connery
Assuming that the direction vectors are with respect to the surface ships
Location vector of Repulse = 4i
Location vector of Bedford = 5j
Let the 2d - equation of the line joining Repulse and submarine be y = mx + c
m = slope = 0-3/4-2 = -1.5
c = y - mx = 1.5 x 4 + 0 = 6
Therefore, y = -1.5x + 6
Let the 2d - equation of the line joining Bedford and submarine be y = ax + b
a = slope = -6-5/18 = -11/18
b = y - ax = 11/18 x 18 - 6 = 5
Therefore, y = -11/18x + 5
The point of intesection of these two lines can be obtained by solving the two equations we get the point x= 1.12359 and y= 4.31462
Therefore the location of the sub = (1.12,4.31,-0.33)
Direction in which the sub is moving is along = (1.12 - 2 )i + (4.31 +1)j = -0.88 i + 5.31j
Distance move in 4 min = distance between the two points = 5.38 x 1000 ft
In 20 min, distance travelled = 5 x 5.38 x 1000 ft = 26912 ft
Therefore magnitude of the vector along which the aircraft has to be sent = 26.912
Direction of the vector is along which the aircraft has to be sent= -0.88 i + 5.31j + k