The speed of the boat on still water is 100km/h. The water flows from the west at a speed of 45km/h. In which direction must the sailor steer the boat in order to fly due to north?
*What I don't understand is 'which way(direction) is the boat travelling?'
Thanks in advance.
Draw the velocity vector v, pointing kind of northwest, with length 100. At its end, add a vector pointing eastward, of length 45.
You want to figure the angle of the velocity vector so that when you add the two, the east-west component is zero. That is, the resultant velocity is due north.
So, if the velocity's direction is θ° west of north, you need
sinθ = 45/100
θ = 26.7°
So, if the pilot steers the boat on a course of 333.3°, he will end up going due north after the water pushes the boat eastward.
To determine the direction in which the boat must be steered in order to travel due north, we need to understand the effect of both the speed of the boat and the speed of the water.
Let's break down the problem:
1. Speed of the boat on still water: This refers to the speed at which the boat would travel if there was no current or flow in the water. In this case, the speed of the boat on still water is given as 100 km/h.
2. Speed of the water flow: This refers to the speed at which the water is flowing. In this case, the water is flowing from the west at a speed of 45 km/h.
Now, to understand the direction in which the boat is traveling, we need to consider the combined effect of the boat's speed and the water flow.
If the boat is traveling directly against the current (i.e., upstream), the speed of the boat relative to land will be reduced. Similarly, if the boat is traveling in the same direction as the flow of the water (i.e., downstream), the speed of the boat relative to land will be increased.
In this case, as the boat is traveling north (i.e., due north), we need to determine the direction in which the boat should be steered in order to counteract the westward flow of the water and maintain a northward direction.
To do this, we can use vector addition. The speed of the boat relative to the water can be found by subtracting the speed of the water flow from the speed of the boat on still water:
Boat's speed relative to water = Speed of the boat on still water - Speed of the water flow
Boat's speed relative to water = 100 km/h - 45 km/h = 55 km/h
Now, imagine the direction of the boat relative to the water as an angle. If the boat were to travel exactly north, the angle would be 0 degrees. In this case, the boat is traveling at an angle to the north, and we need to calculate that angle.
Using basic trigonometry, we can calculate the angle as the inverse tangent (arctan) of the ratio between the vertical component (northward direction) and the horizontal component (westward direction - the speed of water flow):
Angle = arctan(Vertical component / Horizontal component)
Angle = arctan(Boat's speed relative to water / Speed of the water flow)
Angle = arctan(55 km/h / 45 km/h)
Calculating arctan(55/45), we find that the angle is approximately 51.34 degrees.
Therefore, the sailor must steer the boat 51.34 degrees east of north in order to compensate for the westward flow of water and achieve a due north direction.
Remember, this angle calculation assumes a constant flow of water. In reality, the boat will need to continuously adjust its heading to maintain a northern trajectory as the water flow may vary or fluctuate.