Relative Velocity and Position of Ships A and B: Solving for Least Separation

In summary, Ship A is moving at a velocity of 22 km/h towards the south, while Ship B is moving at a velocity of 40 km/h in a direction 37° north of east. The velocity of Ship A relative to Ship B is -31.95 km/h towards the east and -46.07 km/h towards the north. The expression for the position of Ship A relative to Ship B as a function of time is (3.3 + 22t)i + (2.7 - 40sin37°t)j. The separation between the ships is least when t = 0.23 hours and the least separation is 10.24 km.
  • #1
Dante Tufano
34
0
Ship A is located 3.3 km north and 2.7 km east of ship B. Ship A has a velocity of 22 km/h toward the south and ship B has a velocity of 40 km/h in a direction 37° north of east.

(a) What is the velocity of A relative to B?

(b) Write an expression for the position of A relative to B as a function of t, where t = 0 when the ships are in the positions described as above.

(c) At what time is the separation between the ships least?

(d) What is that least separation?


2. Homework Equations : Vaw = Vab + Vbw

3. Okay, so I got the answer for part a, which is -31.95i - 46.07j, but I'm completely lost on the rest of the parts. I have no idea on how to express b in terms of i and j, let alone solve for it, any ideas?
 
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  • #2
Okay, so I figured out part b, but how can I go about doing part c?
 

1. What is relative velocity expression?

The relative velocity expression is a mathematical equation used to calculate the velocity of one object relative to another object. It takes into account the velocity of both objects and the angle between their paths.

2. How is relative velocity expression used in physics?

Relative velocity expression is used in physics to study the motion of objects in relation to each other. It is particularly useful in analyzing situations where objects are moving in different directions or at different speeds.

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

Relative velocity is the velocity of an object in relation to another object, while absolute velocity is the velocity of an object with respect to a fixed point in space. Relative velocity takes into account the movement of both objects, while absolute velocity does not.

4. How do you calculate relative velocity expression?

The relative velocity expression is calculated using the vector addition formula, which takes into account the magnitude and direction of the velocities of both objects. It can also be calculated using trigonometry, by breaking down the velocities into their horizontal and vertical components.

5. In what situations is relative velocity expression most applicable?

Relative velocity expression is most applicable in situations where two or more objects are in motion and their velocities need to be compared. This can include scenarios such as collisions, projectile motion, and relative motion between vehicles.

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