An airplane is traveling at a speed of 650 miles per hour at a bearing of 300 degrees. Once the airplane reaches a certain point, it encounters a wind velocity of 60 miles per hour in the direction of n75degrees W. Find the resultant speed AND direction of the airplane.
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Answers
When an airplane flies in the air which itself is in motion, the velocity of the airplane undergoes a change in relation to the ground. There are two factors --- firstly, a component of the wind velocity which is perpendicular to the direction in wBhich the aircraft is pointing, will make the aircraft fly on a path which would be at an angle to the originally intended direction and, this is called 'drift'. Secondly, a component of the wind velocity that is parallel to the direction in which the aircraft is pointing, will have an effect of increase or decrease in speed of the aircraft.
To understand the concept of drift, imagine a river flowing direct from east to west. A boat on one bank of the river wants to go to a point which lies exactly north of its current location. If it sets its heading exactly towards the north on a compass and continues sailing without looking at the other shore towards the point that it intends to reach, it will finally reach a point which lies a bit towards the west due to the influence of the water flow in the river.
In this question, the aircraft is said to be moving finally in a direction due west, which means a track of 270 degrees at a speed of 350 KMPH. The wind is flowing from North-west, which means from 315 degrees at a speed of 40 KMPH. Since the angle is 45 degrees, the Sine and Cosine are equal, at approximately 70.7% and therefore, the wind component along the track and across the track are equal to 70.7% of 40 KMPH, which is equal to about 28 KMPH. Since the parallel component is against the travel direction, the ground speed is less than TAS and hence, TAS is equal to 343 KMPH. Cross wind component being equal to the same 28 KMPH, Sine of the angle (drift) is equal to 28/343. So, the drift angle is the Sine inverse of that value. The heading would be equal to the track + drift angle since the wind is from the right side. That is, approximately 5 degrees is the drift and the heading is 275 degrees.
Answer:
Velocity of air (wind) = v A =100kmh−1
Velocity of plane w.r.t. air=VPA=300kmh−1
→ → →
vp= v P/A+ VA
The net velocity of the plane will be the vector sum of two velocities.
Velocity of air and velocity of plane w.r.t air. If the plane is to move towards west finally, then the N-S component of velocity should be zero. For this,
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