Distance between Ships A and B after 2 Hours: Solve the Relative Motion Problem

  • Thread starter vbplaya
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In summary, the problem involves determining the distance between two ships after they depart from port. Ship A travels at 20 mph in a direction 30 degrees west of north, while ship B travels 20 degrees east of north at 25 mph. To find the distance, one must calculate the displacement of each ship from its starting point in vector form and then subtract them from each other.
  • #1
vbplaya
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0
relative motion. I've not a clue.

OK I really need help with this problem. I don't even know where to start. If someone could just point me in the right direction, I'd appreciate it. I just need to know where to start. thanks.
Ships A and B leave port together. For the next 2 hrs, ship A travels at 20 mph in a direction 30 degrees west of north while ship B travels 20 degrees east of north at 25 mph.
What is the distance between the 2 ships two hours after they depart?
 
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  • #2
Just find out how far each ship goes and then find its displacement from where it started in vector form. Once you get those two, subtract one from the other tro find the distance.
 
  • #3


To solve this problem, we will use the concept of relative motion. This means that we will consider the motion of one object relative to the other. In this case, we will consider the motion of ship B relative to ship A.

First, we need to draw a diagram to visualize the situation. Let's place ship A at the origin and draw a vector representing its motion at 30 degrees west of north with a magnitude of 20 mph. Then, we can draw another vector representing the motion of ship B at 20 degrees east of north with a magnitude of 25 mph. These vectors will intersect at a point, which represents the position of ship B relative to ship A after 2 hours.

Next, we can use trigonometry to find the components of the vector representing the distance between the two ships. We can use the formula d = vt, where d is the distance, v is the velocity, and t is the time. For ship A, the distance traveled after 2 hours is d = (20 mph)(2 hrs) = 40 miles. For ship B, we can use the components of its velocity to find the distance traveled in the x and y directions. The x component is 25 mph * cos(20 degrees) = 23.7 mph and the y component is 25 mph * sin(20 degrees) = 8.6 mph. Therefore, the distance between the two ships after 2 hours is given by the Pythagorean theorem: d = sqrt((40 mi)^2 + (23.7 mi)^2 + (8.6 mi)^2) = 48.6 miles.

In summary, the distance between ships A and B after 2 hours is approximately 48.6 miles.
 

1. How do you calculate the distance between two ships after 2 hours?

In order to calculate the distance between two ships after 2 hours, you will need to use the formula for relative motion. This formula takes into account the velocities and directions of both ships to determine their relative distance from each other.

2. What information do you need to solve the relative motion problem?

In order to solve the relative motion problem, you will need to know the velocities and directions of both ships, as well as the amount of time that has passed (in this case, 2 hours).

3. How does the direction of the ships affect the distance between them?

The direction of the ships plays a crucial role in determining the distance between them. If both ships are moving in the same direction, the distance between them will increase. However, if they are moving in opposite directions, the distance between them will decrease.

4. Can you use the same formula for calculating the distance between ships that are moving at different speeds?

Yes, the formula for relative motion can be used to calculate the distance between ships that are moving at different speeds. As long as you have the velocities and directions of both ships, you can apply the formula to solve the problem.

5. Is it possible for the distance between the ships to be negative?

Yes, it is possible for the distance between the ships to be negative. This would occur if one ship is moving in the opposite direction of the other ship, and their velocities are such that they are getting closer to each other instead of moving further apart.

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