What is the resultant velocity of the plane if an airplane flying north at 100 meters per second and a boy is walking south on the plane at the speed of 1meter per second?

Answer 1

There's a very subtle point running throughout this question. It's very important to the solution,
but also the source of all kinds of confusion.

The point is: Whenever you talk about speed, it has to be clearly understood "speed with respect to what ?"

Simple example: You're riding in the back seat of a car at 60 miles per hour, and reading a book.
The car is moving at 60 miles per hour with respect to the ground. The book is also moving at
60 miles per hour with respect to the ground, but at zero miles per hour with respect to your lap,
which is why you're able to read it.

In the question here, these "frames of reference" are not stated in the question, but we're sub-consciously
filling them in as we read it. And we come up with something like this:

The airplane is is flying north at 100 meters per second; that's with respect to the ground.
The boy is walking south at 1 meter per second; that's with respect to the floor of the airplane.

Now you want to know the boy's speed. How do you want that ... as measured by the Physicist on the ground,
or the one seated in 26-D in coach ? It makes a big difference.

The physicist on the ground sees the boy moving north at 99 meters per second.

The one seated in coach sees the boy moving south at 1 meter per second.

If the seatbelt sign is on, and the flight attendant is tearing down the aisle to intercept the boy and
roust him back into his seat, and she's running south after him at 5 meters per second down the aisle,
then she sees him moving north at 4 meters per second with respect to herself.

You can see that the frame of reference makes a big difference. If there's any possibility that
it might not be clear from the context, then it has to be stated. Otherwise you have people
getting into a big fight over the answer, because they're speaking different languages but they
don't know it.