Question

St. Louis is 1080 km directly north of New Orleans. A wind is blowing west to east with a speed of 44.7 m/s.

1. (a) What direction should a plane flying from New Orleans to St. Louis head in if the plane

Answer 1

Ans. 1 a)

Vwind = 44.7 m/s

Vplane = 241 m/s

Vnet is the resultant velocity

x is the angle ( or direction of the plane w.r.t the North)

AB = 1080 km

In triangle ABC,

sinx = Vwind / Vplane = 44.7/241

or, x = 10.688^o

So, the plane should fly at angle of 10.688^o to the north.

Ans 2. b)

(Vplane)² = (Vwind)² + (Vnet)²

or, Vnet = sqrt (241² - 44.7²) =236.82 m/s

Time taken = 1080 km / 236.82 m/s = 76 min = 1hr 16 min

Ans 3.c)

In triangle ABC

tan x = Vwind / Vplane = 44.7 / 241

or, x = 10.5^o

Now, plane will reach at point C instead of pont B.

So, tan x = BC/AB

or, BC = 1080 * tan (10.5)^o = 200.166 km

So, plane will reach 200.166 km east of St.Louis.

Ans 4.d)

First, plane will reach at point C,

Vnet = sqrt ( (Vwind)² + (Vplane)² ) = sqrt ( 44.7² + 241² ) = 245.11 m/s

distance covered by plane will be AC,

so, AB/AC = cos x (x = 10.5^o)

or, AC = 1080 km / cos 10.5^o = 1098 km

time taken (t1) = AC / Vnet = 1098 km / 245.11 m/s = 74 min

From, C the plane will travel towards B from east to west

So, its direction will be directly opposite to the wind

Vnet = Vplane - Vwind = (241 - 44.7) m/s = 196.3 m/s

Distance travelled will be CB = 200.166km

time taken (t2) = CB / Vnet = 200.166km / 196.3 m/s = 17 min

So, total time taken by plane to reach at St. Louis = t1 + t2 = 74 min + 17 min = 91 min = 1hr 31 min

Answer 2

a) wind velocity Vw = 44.7 i m/s  
speed of plane is 241 m/s so velocity of plane wrt ground must be in north direction
because plane have to 1080 km innorth .

so one component of plane velocity have to be in west direction so that it wil cancel wind effect and it can fly in north direcvtion .

241cos@ = 44.7     ( @ is angle north of west)

@   =cos(44.7 / 241) = 79.31 degrees    north of west

b) so plane will travel 1080 km in north direction with 241sin79.31 m/s .

t   = 1080 x 10^3 / 241*sin79.31     = 4560.46 sec

c) if plane flies in north direction wind will take it to east direction .

time to reach lastitude = 1080 x 10^3 / 241 = 4481.33 sec

in this time wind will take it to = 44.7 x 4481.33 = 200315.35 m or 200.32 km

d) no plane will have to fly 200.32 in west direction to reach new orleans.

and still wind iis there in east direction .

so effective velocity of plane in west =241 - 44.7 = 196.3 m/s

time to reach = 200.32x 10^3 / 196.3 = 1020.47 sec

total time   = 1020.47 + 4481.33   = 5501.81 sec