An airplane flies betwee two cities separately by a distance `D`. Assume the wind blows directly from one city to the other at a speed `V_(A)(` as shown `)` and the speed of the airplane is `V_(0)` relative to the air. Find the time taken by the airplane to make a round trip between the cities `(` that is , to fly from city `A` to city `B` and then back to City `A )` ?

Options

A. `(2DV_(0))/(V_(0)^(2)-V_(A)^(2))`
B. `(DV_(0))/(V_(0)^(2)-V_(A)^(2))`
C. `(2DV_(0))/(V_(0)^(2)+V_(A)^(2))`
D. `(DV_(0))/(V_(0)^(2)+V_(A)^(2))`

Answer

A

Explanation

The speed of the plane as it goes from city `A` to city `B` is `V_(o)+V_(A)` and the speed of the plane as it goes from city `B` to city `A` is `V_(o)-V_(A)` . Therefore the time taken by the plane to go once the trip is
`t=(D)/(V_(o)-V_(A))+(D)/(V_(o)+V_(A))=(2DV_(o))/(V_(o)^(2)-V_(A)^(2))`