An airplane cruises at 880 km/h relative to the air. It is flying from Denver, Colorado, due west to Reno, Nevada, a distance of 1200 km, and will then return. There is a steady 80 km/h wind blowing to the east What is the difference in flight time between the two legs of the trip?

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zubairpu427 zubairpu427 · Answer 1 · 2020-02-09T14:01:25+01:00

Answer:

The difference of time is 15 minutes.

Explanation:

We should get relative velocity of the trip 1 where wind is blowing in east and airplane is cruising west.

Calculation of first flight

Relative speed = speed of plane - speed of air (as they are moving in opposite direction)

[tex]Vr=880-80\\Vr=800 km/h[/tex]

Time requires for the trip is calculated through equation of velocity

[tex]v=d/t\\t=d/v\\t=1200/800\\t=1.5 h\\t=1.5*60min\\t=90min[/tex]

Calculation of return flight

Now calculate the time for trip two where plane is returning and both wind and plane are now in same direction.

Relative speed = speed of plane + speed of air (as they are moving in same direction)

[tex]Vr=880+80\\Vr=960 km/h[/tex]

Time requires for the trip is calculated through equation of velocity

[tex]v=d/t\\t=d/v\\t=1200/960\\t=1.25 h\\t=1.25*60 min\\t=75 min[/tex]

Difference in flight time

Taking the difference of two flights

Δ[tex]t=90-75\\[/tex]

Δ[tex]t= 15 min[/tex]