Question
A US Coast Guard cutter is chasing a ship suspected of running contraband cigars out of Cuba. The cutter's trip can be divided into three legs: it travels with a constant velocity of 40.1 km/hr for 1 hour and 45.0 minutes at a navigational direction of 260°; then it goes 41.3 km/hr for 51.0 minutes with a navigational direction of 275° and finally, it goes 58.4 km/hr for 33.0 minutes with a navigational direction of 329°. Provide answers in units of km and hours, and assume the cutter started at the origin.
Answers
d = r*t.
d1 = 40.1 km/h * 1.75 h = 70.175km @ 260 deg.
d2 = 41.3 km/h * 51/60 h = 35.105 km @ 275 deg
d3 = 58.4 km/h * 33/60 h = 32.12 km @ 329 deg.
X = hor. = 70.175cos260 + 35.105cos275
+ 32.12cos329,
X = -12.19 + 3.06 + 27.53,
X = 18.4 km.
Y = ver. = 70.175sin260 + 35.105sin275
+ 32.12sin329,
Y = -69.11 + (-34.97) + (- 16.54),
Y = - 120.6 km.
tanA = Y/X = -120.6 / 18.4 = -6.55,
A = -81.3 deg.
R = X/cosA = 18.4 / cos(-81.3) = 121.6
km = Resultant.
d1 = 40.1 km/h * 1.75 h = 70.175km @ 260 deg.
d2 = 41.3 km/h * 51/60 h = 35.105 km @ 275 deg
d3 = 58.4 km/h * 33/60 h = 32.12 km @ 329 deg.
X = hor. = 70.175cos260 + 35.105cos275
+ 32.12cos329,
X = -12.19 + 3.06 + 27.53,
X = 18.4 km.
Y = ver. = 70.175sin260 + 35.105sin275
+ 32.12sin329,
Y = -69.11 + (-34.97) + (- 16.54),
Y = - 120.6 km.
tanA = Y/X = -120.6 / 18.4 = -6.55,
A = -81.3 deg.
R = X/cosA = 18.4 / cos(-81.3) = 121.6
km = Resultant.