An airplane has an airspeed of 500 kilometers per hour bearing N45°E. The wind velocity is 60 kilometers per hour in the direction N30°W. Find the resultant vector representing the path of the plane relative to the ground?

2 Answers
Write your answer here...
Start with a one sentence answer
Then teach the underlying concepts
Don't copy without citing sources
preview
?

Answer

Write a one sentence answer...

Answer:

Explanation

Explain in detail...

Explanation:

I want someone to double check my answer

Describe your changes (optional) 200

4
BeeFree Share
Nov 9, 2015

Answer:

Use unit vectors to solve the addition of two vectors.

Explanation:

Airplane : #500[cos(45)i+sin(45)j]=500[sqrt2/2i+sqrt2/2j]#

Wind : #60[cos(120)i+sin(120)j]=60[-1/2i+sqrt3/2j]#

Next, sum the two vectors:

Sum #=323.5534i+405.5149j#

Angle of resultant vector: #Tan^-1(405.5149/323.5534)~~51.414^o#
or #~~N38.6^oE#

Magnitude of resultant vector: #sqrt(323.5534^2+405.5149^2)~~518.7766# km/hr

Here is a sketch of the plane vector #(AB)# and the wind vector #(AC)#. The resultant vector is #AD#

hope that helped!

enter image source here

Was this helpful? Let the contributor know!
1500
Write your answer here...
Start with a one sentence answer
Then teach the underlying concepts
Don't copy without citing sources
preview
?

Answer

Write a one sentence answer...

Answer:

Explanation

Explain in detail...

Explanation:

I want someone to double check my answer

Describe your changes (optional) 200

1
Nov 9, 2015

Answer:

You'll want to sketch this one out.

Explanation:

The two component forces can be broken down into their vertical and horizontal forces. The plane moves at 45 degrees NE, which means the east component of this force is #500cos(45)# and the vertical component of this force is #500sin(45)#.

The wind moves NW at 30 degrees. The horizontal velocity is #60cos(30)# (in the opposite direction), and vertical is #60sin(30)# in the same direction.
This means that the overall forces if you add and subtract in the vertical and horizontal directions:

Horizontal Velocity will be #500cos(45) - 60cos(30)# to the east
Vertical Velocity will be #500sin(45) + 60sin45# to the North

Was this helpful? Let the contributor know!
1500
Impact of this question
2023 views around the world
You can reuse this answer
Creative Commons License