4) Two surface ships are trying to determine the course and speed of a nearby submarine to prepare for an intercept by a fighter jet. Ship A is located at the point (4, 0, 0) and ship B at the point (0, 5, 0). The coordinates are given in thousands of feet. Ship A determines the location of the submarine to be in the direction of the vector: 21 + 3j - (1/3)k, while ship B locates it in the direction of the vector 18/ – 6j - k. Four minutes prior, the submarine was located at the point (2, -1, -1/3). The fighter jet is due to arrive in 20 minutes. Assuming the submarine moves in a straight line and at a constant speed, what is the position that the surface ships should send to the jet? (Hint: Determine at what time the paths from Ships A and B to the submarine cross. This point in addition to the point located 4 minutes ago will determine the line describing the path of the submarine. The magnitude of this vector will determine the speed of the submarine, in 1000 ft/min.)
4) Two surface ships are trying to determine the course and speed of a nearby submarine to prepare for an intercept by a fighter jet. Ship A is located at the point (4, 0, 0) and ship B at the point (0, 5, 0). The coordinates are given in thousands of feet. Ship A determines the location of the submarine to be in the direction of the vector: 21 + 3j - (1/3)k, while ship B locates it in the direction of the vector 18/ – 6j - k. Four minutes prior, the submarine was located at the point (2, -1, -1/3). The fighter jet is due to arrive in 20 minutes. Assuming the submarine moves in a straight line and at a constant speed, what is the position that the surface ships should send to the jet? (Hint: Determine at what time the paths from Ships A and B to the submarine cross. This point in addition to the point located 4 minutes ago will determine the line describing the path of the submarine. The magnitude of this vector will determine the speed of the submarine, in 1000 ft/min.)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Additional Topics In Trigonometry
Section3.3: Vectors In The Plane
Problem 10ECP
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Transcribed Image Text:4) Two surface ships are trying to determine the course and speed of a nearby submarine to prepare for an
intercept by a fighter jet. Ship A is located at the point (4, 0, 0) and ship B at the point (0, 5, 0). The coordinates are
given in thousands of feet. Ship A determines the location of the submarine to be in the direction of the vector:
2i + 3j - (1/3)k, while ship B locates it in the direction of the vector 18/ – 6j - k. Four minutes prior, the submarine
was located at the point (2, -1, -1/3). The fighter jet is due to arrive in 20 minutes. Assuming the submarine moves
in a straight line and at a constant speed, what is the position that the surface ships should send to the jet?
(Hint: Determine at what time the paths from Ships A and B to the submarine cross. This point in addition to the
point located 4 minutes ago will determine the line describing the path of the submarine. The magnitude of this
vector will determine the speed of the submarine, in 1000 ft/min.)
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