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 resultant velocity of the ship.
To calculate the resultant velocity of the ship, we need to first calculate the velocity of the ship and the velocity of the current in vector form.
The velocity of the ship relative to the water can be calculated as follows:
Vship = 30 km/h (south-westerly) = 30(cos 225° i + sin 225° j) = -21.21 km/h i - 21.21 km/h j
The velocity of the current can be calculated as follows:
Vcurrent = 16 km/h (28° west of north) = 16(cos 28° i - sin 28° j) = 14.35 km/h i - 7.26 km/h j
The resultant velocity of the ship, Vresultant, can be calculated by adding the velocity of the ship and the velocity of the current:
Vresultant = Vship + Vcurrent
Vresultant = (-21.21 km/h i - 21.21 km/h j) + (14.35 km/h i - 7.26 km/h j)
Vresultant = -6.86 km/h i - 28.47 km/h j
Therefore, the resultant velocity of the ship is -6.86 km/h south-east and 28.47 km/h south.