IIT JEE , AIEEE Forum - Physics , Mechanics

neelesh_tripathi

PLEASE SOLVE THIS QUESTION
A plane has to travel from a point A to B 500 km away 30 degrees east of north , wind is blowing @ 20m/s due north and speed of plane is 150m/s find:-
(i)time taken by plane to reach B
(ii)angle made by plane with wind

waterdemon

In this Question The Speed of the aeroplane is

lets say v = 150 m/s 30⁰ east of north

or

We can say 60⁰ north of east

And speed of the wind is 20 m/s

The speed of the wind in the direction

Of the aeroplane = 20Cos 30⁰

So

V₀= New speed of the aeroplane

V₀ = V + 20Cos 30⁰

V₀ = V + 20*

3 / 2

V₀= V + 10

3

V₀ = 150 + 17.3

= 167.3 m/s

So now the Time taken to Reach "B"

S = V₀ T

500 = 167.3 * T

T = 2.9886 s

T

3s

And

2) The angle made by the plane with the Wind is 30^0.

plZ Rate me for my efforts.

Cheers !!!!!!!!!!!!!!!!!!!!!!!!!!!

neelesh_tripathi

THANKS Waterdemon BUT .....

Its still a bit confusing
resultant velocity of plane = sum of 2 vectors wind velocity and velocity of plane

if angle between them is 30 dgrees then the direction of resultant velocity will be between wind V. and plane velocity
then in that case the angle between plane velocity and wind velocity will not be 30 dgrees

waterdemon

See if u go on to take the directions in which they are going then u

may Get confused

You have to find the angle between their Velocity Vectors

For plane V is vel. making 30 deg. with north

For wind it is with V velocity and due noth that is

Along North

So the angle between them becomes 30 Degrees.

Rate me for this if u understood.

Cheers !!!!!!!!!!!!!!!!!!!!!!!!!

Aatish

gud work ...............

ramyani

I also once asked this problem here. For some of the elegant solutions look :
http://www.goiit.com/posts/list/mechanics-verma-problem-on-relative-velocity-13536.htm

neelesh_tripathi

OKAY! Now I get it
THANKS DUDE

joyfrancis

Hi

The point where the pilot has to reach is 30 degrees east of north , now if we

take into account the wind blowing...if the plane heads in that direction only, he

would not land up in the desired spot.

Here is the solution.

Let the angle made by the plane be

degrees east of the line AB.

Net velocity in the x dir Vx=150cos(60-

)

AB=500000m

ABsin30=Vx(t)

150cos(60-

)t=250000.....(1)

velocity in the y direction Vy=150sin(60-

)+20

&ABcos30=250000root3=[150sin(60-

)+20]t....(2)

equations 1 and 2 have 2 variables i.e

and t .

.: sin=1/15 and t=3000s=50min

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