A boat pilot wishes to go in a straight line across a river from the east dock to the west dock in a ferryboat that has a still water speed 8.0 knots. If the river has a Southward current of 2.5 knots, what compass heading should be maintaned while crossing the river? What is the speed of the boat relative to the land?
Pls help me.. I cant understand
To determine the compass heading the boat pilot should maintain while crossing the river, we need to consider both the still water speed of the boat and the current of the river.
Let's break down the problem step by step:
1. Understanding the still water speed: The still water speed of 8.0 knots refers to the speed of the boat relative to the water when there is no current or external force acting on it.
2. Understanding the effect of the current: In this case, the river has a Southward current of 2.5 knots. This means that the current is flowing towards the south at a speed of 2.5 knots.
3. Combining the boat speed and the current: Since the boat is moving across the river, the current will affect its direction and speed. To counteract the effect of the current, the boat needs to point slightly upstream so that its forward motion is in a straight line across the river.
4. Calculating the heading: To determine the compass heading, we can use basic trigonometry. Let's assume the desired heading angle (θ) that the boat should point towards in order to counteract the current.
- The horizontal component of the boat's speed will be the still water speed (8.0 knots).
- The vertical component of the boat's speed will be the current speed (2.5 knots).
- The resultant speed of the boat relative to the ground can be found using the Pythagorean theorem:
Speed (relative to ground) = √[(8.0 knots)^2 + (2.5 knots)^2]
- The angle (θ) can be found using the inverse tangent function:
θ = arctan(vertical component / horizontal component)
Plugging in the values:
θ = arctan(2.5 knots / 8.0 knots)
5. Solving the equation: By calculating the inverse tangent, we find that θ is approximately 17.1 degrees.
Therefore, to maintain a straight line across the river, the boat pilot should maintain a compass heading of approximately 17.1 degrees upstream (northward).
Regarding the speed of the boat relative to the land, we can determine it by using the same Pythagorean theorem equation:
Speed (relative to land) = √[(8.0 knots)^2 - (2.5 knots)^2]
Calculating this, we find that the speed of the boat relative to the land is approximately 7.5 knots.
I hope this explanation helps you understand the problem and how to solve it.