How far downstream has the boat moved?

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In summary, the question asks for the downstream displacement of a boat that is crossing a river with a constant velocity of 9 m/s due north, relative to the water. The river is flowing due east at 1.80 m/s. The velocity of the boat relative to the shore is 9.178 m/s at an angle of 78.69° north of east. To find the downstream displacement, the time it takes the boat to traverse 400 meters in the northern direction at a speed of 9 m/s is calculated first. Then, the boat's downstream displacement in the same amount of time is found by multiplying the time with the velocity. The final answer is 44.4444 seconds, and the correct downstream
  • #1
asloudascanbe
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[SOLVED] How far downstream has the boat moved?

I can't figure out the last part of this question. It's probably very simple and I'm just over looking it. The answers in part A are right. I just don't know how to get part B.

A river flows due east at 1.80 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 9.0 m/s due north relative to the water.

(a) What is the velocity of the boat relative to shore?
9.178 m/s
78.69° (north of east)


(b) If the river is 400 m wide, how far downstream has the boat moved by the time it reaches the north shore?
m
 
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  • #2
1. Find out the time the boat takes to traverse the 400 meters in the northern direction, at speed 9 m/s

2. Then find out the boat's (eastern) dowstream displacement in the same time .
 
  • #3
So to fine the time it takes the boat to go 400 meters at a speed of 9 m/s. I divided 400/9.0 and got 44.4444s.

Then I thought to find the downstream displacement given that time you would just divide the 44.444s/(1.8m/s)? But that's wrong and I don't know what else to do?
 
  • #4
What is distance?

Velocity MULTIPLIED WITH time!
 
  • #5
SOLVED thanks...sorry for some reason I thought you divided it.
 

Related to How far downstream has the boat moved?

1. How is downstream distance calculated?

The downstream distance of a boat can be calculated using the formula: distance = speed x time. In this case, the speed would be the speed of the river current and the time would be the amount of time the boat has been moving downstream.

2. What factors affect the downstream distance of a boat?

The downstream distance of a boat is primarily affected by the speed of the river current, the speed and direction of the boat, and any obstacles in the river such as rocks or debris. Wind speed and direction can also have an impact on the downstream distance.

3. Is the downstream distance the same as the displacement of the boat?

No, the downstream distance and displacement of a boat are not the same. The displacement refers to the straight line distance between the starting point and ending point of the boat's movement, while the downstream distance takes into account the effects of the river current.

4. How can the downstream distance of a boat be measured accurately?

The downstream distance of a boat can be measured accurately using GPS tracking or by timing the boat's movement and calculating the distance based on the speed and time. It is important to take into account any changes in speed or direction during the boat's journey for more precise measurements.

5. Can the downstream distance of a boat be greater than the displacement?

Yes, it is possible for the downstream distance of a boat to be greater than the displacement. This can happen if the river current is strong and the boat is moving at a slower speed than the current. In this case, the boat may travel a longer distance downstream than the straight line displacement between its starting and ending points.

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