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)
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?