How Fast Must a Plane Fly to Overcome Wind from London to Rome?

AI Thread Summary
To determine the velocity a plane must fly to reach Rome from London in 3.5 hours, given a wind speed of 75 km/hr to the east, a vector triangle approach is necessary. The displacement vector from London to Rome is 1400 km at an angle of 42° southeast. Participants in the discussion emphasize the need to construct a vector triangle that includes the wind velocity and the required plane velocity. The correct method involves using trigonometric functions to resolve the vectors and find the unknown velocity. This approach ensures that the plane compensates for the wind while maintaining the intended flight path.
katiefornald
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Homework Statement


The displacement from London to Rome is 1400 km S 42* E. A wind is blowing with a velocity of 75km/hr east. The pilot wants to fly directly from London to Rome in 3.5 hours. What velocity must the plane have relative to the air?


Homework Equations


Sin, Cos, Tan, Cosign law, Sin law


The Attempt at a Solution


I drew a triangle with a 90 degree angle at the bottom left, on the top left is the peak and labeled london which is 43* and the bottom line says 75 km hr which leads to the right to Rome
 
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welcome to pf!

hi katiefornald! welcome to pf! :smile:
katiefornald said:
I drew a triangle with a 90 degree angle at the bottom left, on the top left is the peak and labeled london which is 43* and the bottom line says 75 km hr which leads to the right to Rome

nooo, wrong triangle :wink:

you need a vector triangle whose three sides are all velocities …

75 east, 400 at 42° (or is it 43 °?), and an unknown velocity

you know one angle and two sides, so you should be able to find the third side :smile:
 
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