How Is the Speed of a Man Calculated When Running Across a Boat Moving Upstream?

In summary, a man runs across a boat traveling upstream at 14 km/h with respect to a river flowing at 6 km/h (with respect to the ground) at a speed of 6 km/h. However, since his direction of running is perpendicular to the direction of the boat's movement, his speed with respect to the ground is actually 10 km/h.
  • #1
MathewsMD
433
7
A boat is traveling upstream at 14 km/h with respect to a river that is flowing at 6 km/h (with respect to the ground). A man runs directly across the boat, from one side to the other, at 6 km/h (with respect to the boat). The speed of the man to the ground is ____?

Attempt:

vPG = vPB + vBW + vWG
vPG = 6 km/h + 14 km/h - 6 km/h = 14 km/h

That is not the correct answer, though. The answer is 10 km/h. I keep trying different methods but this seems to be the most correct solution...but it's not.

Any help would be greatly appreciated! :)
 
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  • #2
A man runs directly across the boat, from one side to the other, at 6 km/h
... which direction is he running compared with the direction the boat is moving?
 
  • #3
You'll need to treat the velocities as vectors (taking into account that VPB is perpendicular to VBW and VWG).
 
  • #4
Simon Bridge said:
... which direction is he running compared with the direction the boat is moving?

That is the question word for word, and I agree that it is ambiguous.
 
  • #5
TSny said:
You'll need to treat the velocities as vectors (taking into account that VPB is perpendicular to VBW and VWG).

Okay...I treated it as vBW and vPB as parallel since that's what my impression was from reading the question.

I guess that clears up things quite nicely. Thanks.
 
  • #6
That is the question word for word, and I agree that it is ambiguous.
I don't think it was ambiguous at all - I was trying to direct your attention to the wording.
But you got there in the end.

It can be tricky interpreting word questions. For future reference:

The question says he runs "from one side to the other" ... which would be 90deg to the direction of travel, unless the boat was traveling sideways or something.

The "boat traveling sideways" is the sort of thing the question would make a point of telling you ;)

If he were running parallel to the direction of travel, then he's be going from "front to back" or "from bow to stern" or similar description.
 

FAQ: How Is the Speed of a Man Calculated When Running Across a Boat Moving Upstream?

What is relative velocity?

Relative velocity is the velocity of an object or observer in relation to another object or observer. It takes into account the motion of both objects and their respective velocities.

How is relative velocity calculated?

Relative velocity is calculated by finding the difference between the velocities of the two objects or observers and taking into account their direction of motion. It can be calculated using vector addition or by using the relative velocity formula.

What is the difference between relative velocity and absolute velocity?

Relative velocity takes into account the motion of two objects or observers in relation to each other, while absolute velocity is the velocity of an object or observer in relation to a fixed point or reference frame. Absolute velocity remains constant, while relative velocity can change depending on the motion of the objects involved.

How does relative velocity apply to real-life situations?

Relative velocity is applicable in many real-life situations, such as when calculating the speed of a moving vehicle in relation to another vehicle or when determining the velocity of a swimmer in a river with a current. It is also used in navigation, astronomy, and other fields of science and engineering.

What are some common misconceptions about relative velocity?

One common misconception about relative velocity is that the faster object is always the one with the higher velocity. However, this is not always the case, as the relative velocity also takes into account the direction of motion. Additionally, some people may confuse relative velocity with relative speed, which is the magnitude of the relative velocity without taking into account direction.

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