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

[katiefornald]

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

 

[tiny-tim]

welcome to pf!

hi katiefornald! welcome to pf!

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 …

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 ​