Vector / Relative Motion Problem

[jambliduo]

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?

 

[Redbelly98]

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Welcome to Physics Forums

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.