A riverboat travels with a velocity of 4.60 m/s from one shore to another. The velocity of the river is 2.30 m/s. If the width of the river is 72.0 m, how far does the boat travel downstream to reach the other shore?

Well, if the boat is traveling across the river, it's essentially going against the current since the current is flowing downstream. So, it's like trying to run on a moving walkway in the opposite direction - not the easiest task!

To find out how far the boat travels downstream, we can use the concept of relative velocity. The boat's velocity against the current is the difference between its own velocity and the velocity of the river.

In this case, the boat's velocity against the current would be 4.60 m/s - 2.30 m/s = 2.30 m/s.

Now, to find out the distance, we can use the formula Distance = Velocity x Time. Since we want to find the distance downstream, we can use the velocity of the boat relative to the current, which is 2.30 m/s.

Given that the width of the river is 72.0 m, the time it takes for the boat to cross the river would be Distance/Velocity = 72.0 m / 2.30 m/s ≈ 31.30 seconds.

So, the boat travels downstream for approximately 31.30 seconds. But remember, this is just the time it takes to cross the river, not the total distance traveled by the boat.

To find how far the boat will travel downstream to reach the other shore, we need to find the time it takes for the boat to reach the other shore.

Let's denote the distance traveled downstream as Dd and the velocity of the boat relative to the shore as Vb.
So, Vb = 4.60 m/s (velocity of the boat) - 2.30 m/s (velocity of the river) = 2.30 m/s.

The width of the river is 72.0 m, so the time it takes for the boat to cross the river is given by the formula:
Time = Distance / Velocity

Therefore, the time it takes for the boat to cross the river is:
Time = 72.0 m / 2.30 m/s = 31.3 seconds.

Since the boat is moving downstream, the distance traveled downstream is equal to the velocity of the boat relative to the shore multiplied by the time it takes to cross the river.

So, Dd = Vb * Time
Dd = 2.30 m/s * 31.3 s = 72.19 m.

Therefore, the boat travels approximately 72.19 meters downstream to reach the other shore.

To find the distance the boat travels downstream, we need to first find the time it takes for the boat to cross the river.

Let's assume that the downstream direction is from left to right. The boat's velocity relative to the ground is the vector sum of its velocity relative to the river and the river's velocity.

We can find the time it takes for the boat to cross the river using the equation:

time = distance / velocity.

The distance the boat travels in the upstream direction is the width of the river, which is 72.0 m, and the velocity in the upstream direction is the difference between the boat's velocity and the river's velocity:

velocity upstream = boat's velocity - river's velocity.

Substituting the values, we have:

velocity upstream = 4.60 m/s - 2.30 m/s = 2.30 m/s.

Now, we can calculate the time it takes for the boat to cross the river:

time = 72.0 m / 2.30 m/s.

Dividing 72.0 by 2.30 gives us:

time = 31.30 s.

So, it takes the boat 31.30 seconds to cross the river.

To find the distance the boat travels downstream, we multiply the boat's velocity by the time it takes to cross the river:

distance downstream = boat's velocity × time.

Substituting the values, we have:

distance downstream = 4.60 m/s × 31.30 s.

Multiplying 4.60 by 31.30 gives us:

distance downstream = 144.18 m.

Therefore, the boat travels approximately 144.18 meters downstream to reach the other shore.

you can make this hard (or more general) by setting up distance/speed calculations, and all that, but just notice that

the river's speed is 1/2 that of the boat.

So, the boat goes downstream 1/2 as far as it goes across.