Question

A plane is heading due north and climbing at the rate of 100 km/hr. If its...

A plane is heading due north and climbing at the rate of 100 km/hr. If its airspeed is 470 km/hr and there is a wind blowing 120 km/hr to the northwest, what is the ground speed of the plane?

Homework Answers

Answer #1

Let's use vector notation for solving this problem.

Also, ground speed of plane = airspeed of plane + wind-blowing speed. ..,........... (1)

Let's say unit-vector along west and north direction are i and j respectively.

Then unit cell vector along northwest = (i+j)/√2

Now, airspeed of the plane = (470 kph) j

And, wind blowing speed = (120 kph)*(i+j)/√2

Using formula(1),

Ground speed of plane =  (470 kph)j + (120 kph)*(i+j)/√2

= (84.8528137)i + (554.852814)j kph

So magnitude of ground speed of plane = 561.303521 kph,

Direction from West to North side , = arctan( 554.852814/84.8528137) = 81.30520631° .

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
An airplane heading due north at 500 km/h encounters a wind with a speed of 65...
An airplane heading due north at 500 km/h encounters a wind with a speed of 65 km/h blowing from [N60°E]. Determine the resultant ground velocity of the plane. PLEASE STATE VELOCITY WITH DIRECTION (AND ANGLE)
A pilot must fly a plane due north (90 degrees) to reach a destination. The plane...
A pilot must fly a plane due north (90 degrees) to reach a destination. The plane can fly at 323 km/h in still air. A wind is blowing out of the northeast (225 degrees) at 40 km/h. What is the speed of the plane relative to the ground? The pilot must point the plane to the east of north in order to compensate for the wind speed.
A pilot must fly his plane due north to reach his destination. The plane can fly...
A pilot must fly his plane due north to reach his destination. The plane can fly at 300 km/h in still air. A wind is blowing out of the northeast at 90 km/h. (a) What is the speed of the plane relative to the ground? (b) In what direction must the pilot head his plane to fly due north?
An airplane is headed on a bearing of 170° at an airspeed of 223 km per...
An airplane is headed on a bearing of 170° at an airspeed of 223 km per hr. A 58 km per hr wind is blowing from a direction of 210°. Find the ground speed and resulting bearing of the plane.
An airplane with an airspeed of 600 km/h needs to be on a course 35.0 north...
An airplane with an airspeed of 600 km/h needs to be on a course 35.0 north of east. A steady wind of 100 km/h is blowing FROM the north. Determine the direction the plane should head.
An airplane is heading due south at a speed of 688 km/h If a wind begins...
An airplane is heading due south at a speed of 688 km/h If a wind begins blowing from the southwest at a speed of 90 km/h (average), calculate: (a) the velocity (magnitude and direction) of the plane relative to the ground, and (b) how far from its intended position will it be after 11.0 min if the pilot takes no corrective action. [Hint: First draw a diagram.] (a) VP,G = 628 km/h (b) Dx = 16.5 km  these are the answers...
An airplane is heading due south at a speed of 662 km/h . A wind begins...
An airplane is heading due south at a speed of 662 km/h . A wind begins blowing from the southwest at a speed of 80 km/h (average). In what direction should the pilot aim the plane so that it will fly due south? Express your answer to three significant figures and include the appropriate units.
An airplane flies due north with an air speed of260 km/h . A steady wind at...
An airplane flies due north with an air speed of260 km/h . A steady wind at 65 km/h blows eastward. (Air speed is the speed relative to the air.) What is the plane’s ground speed (vpg)? If the pilot wants to fly due north, what should his heading be?
An airplane with a ground speed of 550 km/hr travels along a heading of 30 degrees...
An airplane with a ground speed of 550 km/hr travels along a heading of 30 degrees N of W. At that high altitude there is a powerful 210 km/hr wind (known as the jet stream) 40 degrees south of west. Determine the direction that the pilot is aiming the plane. The answer key says that the pilot must point 52.4 degrees NofW.
The compass on an airplane indicates it is headed due east, and the airspeed indicator shows...
The compass on an airplane indicates it is headed due east, and the airspeed indicator shows it is moving through the air at 450 km/hr . The wind is blowing 120 km/hr in a direction 30° south of east. (a) What is the velocity of the airplane rel ative to the earth? (b) In what direction should the pilot head for the plane to travel due east? What will be the airplane velocity relative to the earth? Please explain to...