Y:\How to solve 2 dimension relative velocity problems.wpd

ii.
Practice 2: U-531 fires a torpedo at a
freighter in the North Atlantic. The
torpedo travels at 27 knots NW. The
freighter travels at 7 knots 30° S of E.
What is the velocity of the torpedo
relative to the freighter
(1) Component method.
Vector (v) and angle (2)
X-comp
v x = vcos2
Y-comp
v y = vsin2
V tw = 27 kts, 45° V twx = -19.1 V twy = 19.1
V wf = 7 kts, 30° V wfx = -6.1 V wfy = 3.5
Resultant V tfx = -25.2 V tfy = 22.6
Note using your diagram, YOU determine is a component is positive or negative.
v = v + v = ( − 25.2) + (22.6) = 33.8 kts
2 2 2 2
tf tfx tfy
v 22.6
θ = = = °
v −25.2
−1 tfy −1
tan ( ) tan ( ) 41.8 N of W
tfx
(2) Law of sines and cosines
v = v + v −2v v cosθ
2 2
tf tw wf tw wf
v
v
tf
tf
= + − °
2 2
27 7 2(27)(7)cos165
= 33.8kts
β =
v
sinθ
−1
wf
sin ( )
v
−1
7sin165°
β = sin ( ) = 3.1°
33.8
tf
α = 45°− β = 41.9°
N of W