Vector (Relative velocity question)

In summary, the observer on ship A, traveling north at 7km/h, spotted ship B heading southeast at a speed of 12√2 km/h. Using unit vectors and velocity calculations, we can determine that the direction of ship B is E22.6°S. The given answer of N67°23'E is likely a small error, as S67°23'E would be a close approximation of the calculated direction.
  • #1

Homework Statement



An observer, on a ship A sailing to the north with speed of 7km/h, saw a ship B. Ship B seems to be moving to south-east with a speed of 12√2 km/h.

Find the direction which B is heading to.

Homework Equations


The Attempt at a Solution



Let i and j be the unit vectors in the direction of eat north respectively and VA = velocity of ship A and VB = velocity of ship B.

Now, VA = 7j

BVA = 12i - 12j

VB
= BVA + VA
=12i - 5j

so θ = tan-15/12 = 22.6°

The direction of ship B is E22.6°S.

But the answer given is N67°23'E, which step is incorrect? Can anyone enlighten me?
 
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  • #2
Michael_Light said:
The direction of ship B is E22.6°S.

But the answer given is N67°23'E, which step is incorrect? Can anyone enlighten me?
Your answer looks fine to me. Are you sure the book's answer wasn't S67°23'E, which would be pretty close to yours.
 

1. What is a vector?

A vector is a mathematical representation of a quantity that has both magnitude (size) and direction. It can be represented graphically by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction.

2. What is relative velocity?

Relative velocity is the measurement of the velocity of one object with respect to another. It takes into account the motion of both objects and their respective velocities in relation to each other.

3. How do you calculate relative velocity?

To calculate relative velocity, you need to first determine the velocities of both objects. Then, you can use vector addition or subtraction to find the relative velocity. If the objects are moving in the same direction, you add their velocities. If they are moving in opposite directions, you subtract their velocities.

4. What is the difference between speed and velocity?

Speed is a scalar quantity that measures how fast an object is moving, while velocity is a vector quantity that measures the rate of change of an object's position. Velocity includes both speed and direction, whereas speed only considers magnitude.

5. How is relative velocity used in real life?

Relative velocity is important in many real-life scenarios, such as in navigation, aviation, and driving. It is also used in sports, such as calculating the speed of a baseball thrown by a pitcher or the velocity of a soccer ball kicked by a player. In addition, it is used in physics and engineering to analyze and understand the motion of objects in relation to each other.

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