An airplane pilot sets a compass course due west and maintainsan airspeed of 220 km/h. After flying for 0.500 h, she find sherself over a town 120 km

melodykap

melodykap

Answered question

2021-02-03

An airplane pilot sets a compass course due west and maintainsan airspeed of 220 km/h. After flying for 0.500 h, she find sherself over a town 120 km west and 20 km south of her starting point. a) Find the wind velocity (magnitude and direction). b) If the wind velocity of 40 km/h due south, in what direction should the pilot set her course to travel due west? Use the same airspeed of 220 km/h. 
The answers are: 
a) 44.7 km/h, 26.6 deg. west of south 
b) 10.5 deg. north of west

Answer & Explanation

Anonym

Anonym

Skilled2021-02-04Added 108 answers

If there is no wind then theplane would be at a distance
d=(220 km/h)(0.5h)=110km west of the starting point.
if the wind is blown then then the plane is 120km-110km=10km west and 20km south in the time 0.5h.
Velocity of the plane in west direction=(10km)/0.5h=20km/h
velocity of the plane in south direction=(20km)/0.5h=40km/h
Now the wind velocity is
(20kmh)2+(40kmh)2=44.7kmh
the direction is
θ=tan1(40kmh20kmh)=63
south of west
b) If the wind velocity is 40km/h then the direction is
θ=sin1(40kmh220kmh)=10.5
north of west
Jeffrey Jordon

Jeffrey Jordon

Expert2021-09-28Added 2605 answers

The velocity of the plane relative to earth is given by

VP/E=dt=120i^20j^0.5=[240i^40j^] km/h

According to relative motion the velocity of the air relative to the earth is given by

VA/E=VP/EVP/A

=240i^40j^(220i^)

=[20i^40j^] km/h

The magnitude v_{A/E} is given by

vA/E=(40)2+(20)2=44.7 km/h

the angle θ1 is given by

θ1=arctan(4020)=63.4

But the angle is in 3rd quadratic so add 180

θ1=180+63.4=243.4

b)In this case the captain want to move with 220 km/h toward west relative to earth and wind blow in 40 km/h toward south relative to earth too , so the vectors are given by :

VP/E=[220i^] km/h

VA/E=[40j^] km/h

The relative velocity VP/A is given by

VP/A=VP/EVA/E

=220i^(40j^)

=[220i^+40j^] km/h

The magnitude vP/A is given by

vP/A=(220)2+(40)2=223.6 km/h

The angle θ1 is also given by

θ2=arctan(40220)=10.3

The angle θ2 is in 2nd quadratic so add 180 to get it with respect to +x -axis

θ2=18010.3=169.7

Or we can say 10.3 north of west

 

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Electromagnetism

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?