Question

Vectors! A ship can sail at 30 km/h in still water. The ship heads due north. The water current is flowing at 10 km/h due east.

a) What is the actual velocity of the ship?

b) What direction does the ship sail in?

Answer 1

• a) 31.62 km/h
• b) 18.4° NE

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Given

• The speed of the ship = 30 km/h,
• The speed of the current = 10 km/h

A) Actual velocity is found as the sum of two vectors representing the two velocities.

Since the directions are at 90° (N and E), we will use Pythagorean to find the actual velocity.

• 
  `v = √(30^2+10^2)=√(1000)= 31.62` km/h (rounded)

b) Let the direction the ship sails in is x. Use trigonometry to find the angle from the North:

• tan x = 10/30
• tan x = 1/3
• x = arctan (1/3)
• x = 18.4° NE