Relative motion problem with airplane and wind velocity

In summary, the plane should fly at an angle of w west of south in order to reach point B in time for the given wind speed.
  • #1
Stormblessed
24
2

Homework Statement


A small airplane wants to fly from A to B which is 200 km due south. The wind is blowing towards the east at a velocity of 50 km/h. If the airplane can move through the air at 300 km/h, find the direction the plane should be heading; the speed of the airplane relative to the ground; the time it will take to reach point B.

Homework Equations


p is plane, g is ground, w is wind
Vpg = Vpw + Vwg

The Attempt at a Solution


I wrote out the givens to start:
V = 300 km/h
d = 200 km
Vwg = 50 km/h [E]
Vpg = ?

I do not really know where to go from here. I understand that only one vector with both direction and magnitude is given (Vwg). The velocity of the plane is only a magnitude with no direction. I was unable to draw a vector diagram because I don't know what it should look like to accurately represent the scenario.
 
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  • #2
So the wind is blowing from the West. The plane will need to fly at an angle west of south.
If that angle is w, then the velocity south will be 300 cos(w) k/h and the velocity west will be 300 sin(w) k/h plus the speed of the wind (-50 k/h).
So you need to make that east/west velocity zero and then work from there.
 
  • #3
.Scott said:
So the wind is blowing from the West. The plane will need to fly at an angle west of south.
If that angle is w, then the velocity south will be 300 cos(w) k/h and the velocity west will be 300 sin(w) k/h plus the speed of the wind (-50 k/h).
So you need to make that east/west velocity zero and then work from there.

I'm still unsure how to solve it; can you describe the next few steps please?
 
  • #4
Set up the equation for the east/west speed, set it to zero, then solve for cos(w).
 
  • #5
Stormblessed said:
I'm still unsure how to solve it; can you describe the next few steps please?
.Scott said:
Set up the equation for the east/west speed, set it to zero, then solve for cos(w).

I got this equation: 300cos + 300sin - 50 = 0
 
  • #6
I got 300sin(w)-50 = 0
 

Related to Relative motion problem with airplane and wind velocity

What is the concept of relative motion in regards to an airplane and wind velocity?

The concept of relative motion refers to the movement of an object in relation to another object. In the case of an airplane and wind velocity, the airplane's motion is affected by the wind's motion, creating a relative motion between the two.

How does wind velocity affect an airplane's motion?

Wind velocity can affect an airplane's motion in several ways. If the wind is blowing in the same direction as the airplane, it can increase the airplane's speed. If the wind is blowing in the opposite direction, it can decrease the airplane's speed. Additionally, wind can also cause the airplane to drift off course if it is not compensated for by the pilot.

How do you calculate the net velocity of an airplane in relation to wind velocity?

To calculate the net velocity of an airplane in relation to wind velocity, you must first determine the individual velocities of the airplane and the wind. Then, you can use vector addition to find the resultant velocity, which is the net velocity of the airplane in relation to the wind.

What factors can influence the relative motion between an airplane and wind velocity?

The relative motion between an airplane and wind velocity can be influenced by various factors, such as the speed and direction of the wind, the speed and direction of the airplane, and the angle at which the wind is blowing in relation to the airplane's direction of travel.

How can pilots compensate for wind velocity when flying?

Pilots can compensate for wind velocity when flying by adjusting the angle and speed of the airplane, as well as using navigational instruments to track and adjust for the effects of wind. They can also use techniques such as crabbing and side-slipping to maintain control and stay on course when flying in windy conditions.

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