Question

A sailboat runs before the wind with a constant speed of 2.8 m/s in a direction 52° north of west. How far (a) west and (b) north has the sailboat traveled in 35 min?

Answer 1

Displacement along west = 3612 m

Displacement along north = 4633.50 m

Explanation:

Let east be positive x axis and north be positive y axis

Velocity of boat = 2.8 m/s in a direction 52° north of west.

Velocity, v = -2.8 cos 52 i + 2.8 sin 52 j = -1.72 i + 2.21 j m/s

Time taken = 35 min = 35 x 60 = 2100 s

Displacement = Velocity x Time

Displacement =  (-1.72 i + 2.21 j)  x 2100

Displacement =  -3612 i + 4633.50 j m

Displacement along west = 3612 m

Displacement along north = 4633.50 m