1. A ship has a top speed of 3.0 m/s in calm water. The current of the ocean tends to push the boat at 2.0 m/s on a bearing of due South. What will be the net velocity of the ship if the captain points his ship on a bearing of 55 North or West and applies full power?

Answer 1

Vs = 3m/s[135o] + 2m/s[270o]

X = 3*cos135 = -2.12 m/s.
Y = 3*sin135 + 2*sin270o = 0.1213 m/s.

Tan Ar = Y/X = 0.1213/-2.12 = -0.05723
Ar = -3.275o = Reference angle.
A = -3.275 + 180 = 176.7o

Vs = X/cosA = -2.12/cos176.7=2.123 m/s.
[176.7o]