Vector / Relative Motion Problem

In summary, the pilot flies east from Hartford to Providence and releases a balloon directly over Providence. After 15 minutes, the pilot turns around and sees the balloon again over Hartford. The approximate wind velocity can be calculated by writing equations for the flight times of the different segments of the trip and solving for the unknown velocity.
  • #1
jambliduo
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Homework Statement



A pilot flying East from Hartford to Providence (distance of 50 miles) releases a balloon directly over Providence. 15 minutes later, the pilot turns around. The pilot sees the balloon again over Hartford. What is the approximate wind velocity? (Assume constant airspeed for the plane)

Homework Equations



Basic kinematic equations: https://www.physicsforums.com/showpost.php?p=905663&postcount=2
Vector Addition / Components

The Attempt at a Solution



The balloon travels 50 miles W. Meanwhile, the pilot travels 15 minutes E and then turns back around. 15 minutes later, he's back over Providence. So, it took 30 minutes for him to get back to where to he released the balloon. He now travels 50 miles W back to Hartford. When he reaches Hartford, he sees that the balloon has traveled the 50 miles from Providence in the same amount of time it took the pilot to travel the 50 miles plus an additional 30 minutes.

So, the pilot completed the 50 mile trip from Providence to Hartford 30 minutes faster than the balloon did. Thus, the pilot's velocity is faster than the wind velocity by 30 minutes.

What I can't seem to figure out is how to calculate either the wind or the plane velocity. For the part that we have distance, we don't have time. For the part that we have time, we don't have distance. How would I combine the two to get wind velocity?
 
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jambliduo said:

Homework Statement



A pilot flying East from Hartford to Providence (distance of 50 miles) releases a balloon directly over Providence. 15 minutes later, the pilot turns around. The pilot sees the balloon again over Hartford. What is the approximate wind velocity? (Assume constant airspeed for the plane)


Homework Equations



Basic kinematic equations: https://www.physicsforums.com/showpost.php?p=905663&postcount=2
Vector Addition / Components

The Attempt at a Solution



The balloon travels 50 miles W. Meanwhile, the pilot travels 15 minutes E and then turns back around. 15 minutes later, he's back over Providence.
You are ignoring the fact that there is a wind. It does not take the same amount of time to fly east and then west again over the same distance.
So, it took 30 minutes for him to get back to where to he released the balloon. He now travels 50 miles W back to Hartford. When he reaches Hartford, he sees that the balloon has traveled the 50 miles from Providence in the same amount of time it took the pilot to travel the 50 miles plus an additional 30 minutes.

So, the pilot completed the 50 mile trip from Providence to Hartford 30 minutes faster than the balloon did. Thus, the pilot's velocity is faster than the wind velocity by 30 minutes.

What I can't seem to figure out is how to calculate either the wind or the plane velocity. For the part that we have distance, we don't have time. For the part that we have time, we don't have distance. How would I combine the two to get wind velocity?
I suggest writing what is going on in the form of equations. The equations are statements about different segments of the trip, for example:

1. An equation describing the flight time of the eastward (from Providence) segment of the flight
2. An equation describing the flight time of the entire westward segment of the flight
3. An equation describing the flight time of the balloon's westward motion

Writing down equations like that is a first step to figuring out what is going on.
 

FAQ: Vector / Relative Motion Problem

1. What is vector motion?

Vector motion is the movement of an object in a specific direction and with a specific magnitude. This means that instead of just considering the distance an object has traveled, we also take into account its direction of motion. Vectors are represented by arrows, with the length of the arrow representing the magnitude and the direction of the arrow indicating the direction of motion.

2. What is relative motion?

Relative motion refers to the movement of an object in relation to another object. It is the difference between the velocities of two objects. For example, if you are sitting in a moving car, your relative motion to the car is different than your relative motion to objects outside the car.

3. How do you solve a vector/relative motion problem?

To solve a vector/relative motion problem, you need to first identify all of the given information, such as velocities, directions, and distances. Then, you can use vector addition and subtraction to find the net velocity of the object. It is important to pay attention to the direction of the vectors and use the correct mathematical operations to solve the problem.

4. What is the difference between speed and velocity in vector motion?

Speed and velocity are often used interchangeably, but they have different meanings in vector motion. Speed is a scalar quantity that only considers the magnitude of motion, while velocity is a vector quantity that takes into account both the magnitude and direction of motion. This means that an object can have the same speed but different velocities if it is moving in different directions.

5. How do you handle acceleration in a vector/relative motion problem?

Acceleration is the rate of change of velocity over time. In vector/relative motion problems, acceleration can be handled by considering it as a separate vector. You can use the equations of motion to calculate the final velocity of the object after a given time or the distance it has traveled during that time. It is important to keep in mind the direction of acceleration and how it affects the net velocity of the object.

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