Relative velocity ship problem intuitively

In summary, the problem involves two ships, A and B, with A moving east at a velocity of 8 km/hr and B moving south at a velocity of 6 km/hr. The question asks for the magnitude of A's velocity in relation to B and the closest distance between the two ships. To solve for the closest distance, the relative velocity of A with respect to B is used, represented by AE. By drawing a triangle with AB as the given distance of 4 km, the angle x is solved for using the sine function. The closest distance, BD, is then found by multiplying sin x by AB.
  • #1
anurag07
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Homework Statement


Two ships A and B are 4 km apart. A is due west of B. If A moves with uniform velocity of 8 km/hr due east and B moves with a uniform velocity of 6 km/hr due south. Calculate 1) the magnitudeof the velocity of A in relation to B 2) the closest distance apart of A and B

Homework Equations


The first solution is pretty simple but the second one, I don't get it. I know how to just solve it but without any intuition. Can someone help me get an intuitive idea of the solution of 2) ? The solution will be down there.

The Attempt at a Solution


In the example BD is drawn from B to relative velocity of A with respect to B represented by AE. From the given distance between A and B is 4km i.e. AB = 4km. In ABE sin x = BE/AE = 6/10 ( x= Angle EAB, BE = Velocity of B in opposite direction, AE = relative velocity of A in respect to B )
x=36.67
Closest distance apart from A to B is BD.
Now in BDA,
BD = sin x * AB = sin 36.87 * 4 = 2.4 km
This is the closest distance.
 

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  • #2
Posting tiny sideways pics is not a good way to get people to look at them.
 
  • #3
phinds said:
Posting tiny sideways pics is not a good way to get people to look at them.
Dont have a good phone. Sorry. And vertical pictures are even tinier.
 
  • #4
The idea is to use B's reference frame. In that frame, what are the NS and EW components of A's motion. At what point does B perceive A as being at closest approach?
 
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1. What is relative velocity in a ship problem?

Relative velocity in a ship problem refers to the concept of how an object's motion is perceived from the perspective of another moving object, such as a ship. It takes into account both the velocity of the object in motion and the velocity of the observer, and can be calculated using vector addition.

2. How is relative velocity calculated in a ship problem?

To calculate relative velocity in a ship problem, you need to first determine the velocity of the ship and the object in motion. Then, using vector addition, you can add the two velocities together to get the relative velocity. This can be done using the Pythagorean theorem or by breaking down the velocities into their respective components.

3. What is the difference between relative velocity and absolute velocity in a ship problem?

The main difference between relative velocity and absolute velocity in a ship problem is that relative velocity takes into account the observer's perspective, while absolute velocity does not. Absolute velocity only considers the motion of the object itself, while relative velocity takes into account the motion of both the object and the observer.

4. How does the direction of the observer affect relative velocity in a ship problem?

The direction of the observer can greatly affect the relative velocity in a ship problem. If the observer is moving in the same direction as the ship, the relative velocity will be greater than if the observer is moving in the opposite direction. This is because the observer's motion adds to or subtracts from the ship's velocity, depending on their direction.

5. How can understanding relative velocity in a ship problem be useful in real-life situations?

Understanding relative velocity in a ship problem can be useful in many real-life situations, such as navigation and transportation. It can help determine the most efficient route for a ship to take, taking into account the motion of the ocean currents and the ship itself. It can also be used in air traffic control to calculate the relative velocity of different aircrafts and avoid collisions. Additionally, it is a fundamental concept in understanding the motion of objects in space and is used in space missions and satellite navigation systems.

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