A ship that can cruise at a speed of 30 km/h in still waters sets a south- westerly course. It is driven off course by a current flowing 28° west of north at 16 km/h. Calculate: 4.1 The distance the ship traveled after 3 hours
To solve this problem, we can break down the ship's velocity into two components: one in the south direction and the other in the west direction.
The southward component of the ship's velocity is given by:
V_south = 30 km/h * sin(28°) ≈ 30 km/h * 0.479 = 14.37 km/h
Similarly, the westward component of the ship's velocity is given by:
V_west = 30 km/h * cos(28°) ≈ 30 km/h * 0.878 = 26.34 km/h
The ship's distance traveled after 3 hours can be calculated by adding up the distances traveled in the south and west directions separately:
Distance_south = 14.37 km/h * 3 hours = 43.11 km
Distance_west = 26.34 km/h * 3 hours = 79.02 km
The total distance traveled by the ship after 3 hours is the hypotenuse of the right triangle formed by the southward and westward distances:
Distance_total = sqrt((Distance_south)^2 + (Distance_west)^2)
Distance_total = sqrt((43.11 km)^2 + (79.02 km)^2)
Distance_total = sqrt(1857.66 km^2 + 6241.61 km^2)
Distance_total = sqrt(8099.27 km^2)
Distance_total = 89.99 km
Therefore, the ship traveled approximately 89.99 km after 3 hours.