Hey Everyone,
If Possible need some help with the following Question. I have attempted (1) and (2) and need some help on (3). Thanks. Any Contribution will be appreciated.
A plane can fly at 350 km/h in still air. The pilot wishes to fly from airport A to airport B where AB= (2000i + 5000j) km
1)
1) There is a wind blowing with velocity ( 30i – 20j) km/h. Find the velocity vector, in the form ai + bj, which the pilot should set so that the plane flies directly from A to B.
My Working Out:
AB = p + w
λ(2000i +5000j) = (ai+bj) + (30i-20j)
2000iλ + 5000jλ = (a+30)i + (b-20)j
a+30 = 2000λ ... (1)
b-20 = 5000λ ... (2)
(2)/(1) =
b-20/a+30 = 2.5
b-20 + 2.5 a + 75
b = 2.5 a + 95
__
a2 + b2 = 3502
a2 + (2.5a + 95 ) 2 = 3502
a2 + 6.25a2 + 475a + 9025 = 122500
7.25 a2 + 475a – 113475 = 0
Using the quadratic equation
a = 96.56 and a = - 162.083
b = 2.5 (96.56 ) + 95 = 336.4
b = 2.5 (- 162.083) + 95 = -310.2075
Therefore p = -310i + 336j km/h
2)
How Long will this flight take?
Velocity = Distance / Time
Time = Distance / Velocity
Time = Square Root of [(-310)^2 + (336)^2]
=457 km
Time = 457 / 350 = 1.306
Time = 1 hour and 18 Minutes
3)
a)How long will it take for the plane to fly from A to B in still air?
Thankyou.