Need help with 3d relative velocity h/w problem

In summary: A and B as the points of the hypotenuse and C was a point on the line between themIn summary, a swimmer wants to cross a river from point A to point B. The distance from A to C is 200 m and the distance from C to B is 150 m. The speed of the current in the river is 5 km/h and the swimmer makes an angle of 45 degrees with respect to the line from A to C. The question is, what speed should the swimmer have relative to the water to swim directly from A to B? This can be solved using the equation: velocity vector (swimmer with respect to earth) = velocity vector (swimmer with respect to river) +
  • #1
dk702
6
0
Here the question,

A swimmer wants to cross a river, from point A to point B. The distance d_1 (from A to C) is 200 m, the distance d_2 (from C to B) is 150 m, and the speed v_r of the current in the river is 5 km/h. Suppose that the swimmer makes an angle of theta=45 deg. (0.785 radians) with respect to the line from A to C.


To swim directly from A to B, what speed v_s, relative to the water, should the swimmer have?

I think this is the eq. i need. velocity vector(swimmer with respect(wrt) to earth)= velocity vector(swimmer wrt river)+ velocity vector(river wrt earth)

my values so far, that I know are wrong

v_(s/e)=9km/hr
v_(r/e = 5km/hr
v_(s/r)= 7.5

If the swimmer wanted to swim from A to C i could solve it. It is that he wants to swim from A to B that is giving trouble.

To give you an idea of my skill level:
I can solve a problem such as this;

The compass on an airplane indicates it is heading due north and its airspeed indicator shows that it is moving through the air at 240km/h. If there is a wind of 100km/h from the west, what is the velocity of the plane relative to the earth? What direction should the pilot head to travel due north and what will be his velocity relative to the Earth then?

v_(p/e)=260km/h at 23 deg E of N

and v_(p/e) = 218km/h at 25 deg W of N
 
Last edited:
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  • #2
Where is C in relation to A and B??

You say that "The distance d_1 (from A to C) is 200 m, the distance d_2 (from C to B) is 150 m " but that doesn't help unless we know the angles formed. Is C on the line from A to B? That would be the easiest case: Then just ignore C and take the distance from A to B to be 350 m but surely it's not that simple.
 
  • #3
Originally posted by HallsofIvy
Where is C in relation to A and B??

You say that "The distance d_1 (from A to C) is 200 m, the distance d_2 (from C to B) is 150 m " but that doesn't help unless we know the angles formed. Is C on the line from A to B? That would be the easiest case: Then just ignore C and take the distance from A to B to be 350 m but surely it's not that simple.
i think he could be talking of a triangle...I should know how to do this... i'll need to find my maths brain...
 
  • #4
But none of "knows how to do it" until we know where C is!
 
  • #5
Originally posted by HallsofIvy
But none of "knows how to do it" until we know where C is!
I was meaning if it was a triangle
 

1. What is relative velocity?

Relative velocity is the measure of the motion of an object with respect to another object. It takes into account the velocity of both objects and their direction of motion.

2. How is relative velocity calculated?

Relative velocity is calculated by subtracting the velocity of one object from the velocity of the other object. The direction of motion also needs to be taken into account when calculating relative velocity.

3. What is the difference between relative velocity and absolute velocity?

Absolute velocity is the velocity of an object with respect to a fixed reference point, while relative velocity is the velocity of an object with respect to another moving object. Absolute velocity remains constant, while relative velocity can change depending on the motion of the other object.

4. Can relative velocity be negative?

Yes, relative velocity can be negative. This means that the two objects are moving in opposite directions with respect to each other.

5. How can relative velocity be applied in real life?

Relative velocity has many applications in real life, such as in navigation, astronomy, and transportation. For example, airplanes must take into account their relative velocity with respect to the wind in order to reach their destination accurately.

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