Vectors In Component Form

**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(2000**i** +5000**j**) = (a**i**+b**j**) + (30**i**-20**j**)

2000**i**λ + 5000**j**λ = (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.

Re: Vectors In Component Form

Do you still want help? :P

Re: Vectors In Component Form