Aeroplane flight: time, displacement, velocity question

In summary, the problem involves an airplane making a round trip between two airports on the same line of longitude. On the first day, there is no wind and the plane travels with constant speed v, completing the round trip in time T0. On the following day, there is a wind blowing at speed kv at an angle z to the line connecting the airports. The pilot maintains the same speed v relative to the air, resulting in a round trip time of T. The task is to find T/T0. Using the equation Speed=distance/time, it can be determined that the round trip distance is vT0. The answer can be found using the formula T/T0 = [(1-k^2(sin^2 z))^0.
  • #1
nathangrand
40
0
1. Homework Statement

An aeroplane makes a round trip between two airports A and B located on the same line of longitude. On a windless day the aeroplane travels with constant speed v and the round trip time is T0. On the following day the same journey is made but there is a wind blowing at speed kv (k<1) at an angle z to the line AB. The pilot maintains the same speed v relative to the air and always flies along the line AB and BA. The round trip time is now T (neglecting take offs, landings and stopovers)

Find T/T0


Homework Equations



Speed=distance/time


The Attempt at a Solution



Know that the distance for a round trip is vT0
Know that the speed will be different for A to B than B to A
Know that the answer is T/T0 = [(1-k^2(sin^2 z))^0.5]/(1-k^2)

When considering an angle of z=0 can get an answer of 1/(1-K^2) which is consistent with the above general answer

I just am not sure how to find the speeds relative to the ground with the wind at an angle?
 
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  • #2
hi nathangrand! :smile:

(try using the X2 icon just above the Reply box :wink:)

draw a vector triangle for each of the two journeys, then join the two triangles together and do a bit of trig :smile:
 

1. How long does it take for an aeroplane to reach its destination?

The time it takes for an aeroplane to reach its destination depends on various factors such as the distance of the destination, the speed of the aeroplane, and any potential delays. Generally, a commercial aeroplane can travel at an average speed of 550 miles per hour, so a flight of 1,000 miles would take approximately 2 hours.

2. How is displacement calculated for an aeroplane in flight?

Displacement is the distance between the starting point and the ending point of an object. In the case of an aeroplane in flight, displacement is calculated by measuring the distance between the aeroplane's starting point (airport of departure) and the ending point (airport of arrival).

3. What is the average velocity of an aeroplane during a flight?

The average velocity of an aeroplane during a flight can vary depending on factors such as wind speed and direction. However, on average, a commercial aeroplane can travel at a speed of 550 miles per hour. This can also be affected by the type of aeroplane, its engine power, and the altitude it is flying at.

4. How does air resistance affect an aeroplane's flight time?

Air resistance, also known as drag, can affect an aeroplane's flight time by slowing it down and requiring more fuel to maintain its speed. This is why aeroplane designs are streamlined to reduce drag and increase efficiency. Additionally, weather conditions such as strong headwinds can also increase air resistance and potentially extend the flight time.

5. Can an aeroplane's velocity change during a flight?

Yes, an aeroplane's velocity can change during a flight. Factors such as wind speed and direction, air traffic control instructions, and turbulence can all impact an aeroplane's velocity. Pilots also have the ability to control the velocity of the aeroplane through their use of throttle and flaps.

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