Can you help me with this question, too?
Suppose that the boat is supposed to arrive at a point directly across the river from its starting point.
a) What should be the heading of the boat?
There is not enough information, was there a previous question or other info?
The river flowed at 10 km/hr
the boat went at 24 km/hr
The boat must head upstream such that 24 sin T = 10
or T = 24.6 degrees upstream of straight across
By the way, his speed across the river is now 24 cos 24.6 degrees = 21.8 km/hr
By the way, this is why you swim aiming toward the other bank and let yourself be swept downstream. If you try to head enough upstream to make a path straight across to a selected spot on the other bank, you will take longer getting across assuming you do not mind landing downstream on the other bank.
In the limit, as the current reaches your swimming speed, you will never reach the other side, whereas if you just aim for the other bank and let the current take you as it wishes, at least you will get to the other side if somewhat downstream.
The answer says 65 degrees upstream. I don't know how they got that.
Well, I did 24.6, call it 25 degrees from straight across.
That is 90 - 25 = 65 degrees from the bank.
I think the question was designed by a mathematician, not a navigator :)
Sure, I can help you with that question!
To determine the heading of the boat, we need to understand the concept of relative velocity.
When a boat is moving across a river, it experiences two velocities: its own forward velocity (the speed with which it moves through the water) and the velocity of the river flow. The resulting velocity of the boat is a combination of these two vectors.
To arrive at a point directly across the river from its starting point, the boat needs to counteract the lateral drift caused by the river flow. This means the boat should point slightly upstream to compensate for the river's current.
In general, the boat's heading should be calculated using the trigonometric concept of vector addition. Here's how you can do it:
1. Determine the speed of the river current. Let's say it is represented by Vr.
2. Calculate the boat's forward velocity. Let's denote it as Vb.
3. Find the angle between the boat's heading and the river current. This angle can be calculated using the inverse tangent function (arctan) and is given by θ = tan^(-1)(Vr / Vb).
So, to answer the question:
a) The heading of the boat should be pointed at an angle θ, as calculated using the formula θ = tan^(-1)(Vr / Vb).
Keep in mind that this calculation assumes idealized conditions and a constant river flow. In most real-world scenarios, the boat will need to continuously adjust its heading to account for changes in current and wind conditions to arrive exactly across the river.