Problem 5.2: A plane approaches JFK for Landing from M miles away from the airpo
ID: 1264897 • Letter: P
Question
Problem 5.2: A plane approaches JFK for Landing from M miles away from the airport. This distance is a straight-line distance linking this current plane position and JFK. Wind blows at a constant speed w and at a direction perpendicular to the straight-line. The plane flies at a constant speed v0 > w relative the wind and it maintains its heading directly toward to WK at all times. Due to the wind, the plane must travel on a curved trajectory whose length is bigger than M Now, we assume the plane has enough fuel to travel precisely 15M miles Derive the relationship for M, v0. w with which the plane can land without running out of fuel.Explanation / Answer
Relative velocity of the plane is 'v0'
Therefore, the absolute velocity, v = (v0^2 - w^2)^0.5 ------ Eqn 1
Assuming the amount of fuel used per unit time is independent of velocity,
M/v = 1.5M/v0
or, v0/v=1.5 ----- Eqn 2
Solving the two equations we get,
v0 = 1.34w
v = 0.89w