Description: An airplane is flying from San Francisco to Seattlewhich is a distance of approximately 1200 km. The cruising speed ofthe plane (VP ) is 400 km/hr relative to the air, and on a calm day(no wind) the pilot would fly on a path, due north, arriving inSeattle exactly 3.0 hours after leaving San Francisco(ignoring thetime spent taxiing, taking off, landing etc.). However, today, thewind is blowing due east with a constant velocity (VW) of 50 km/hrrelative to the ground, and the pilot has not taken this intoaccount. Without paying attention, the pilot keeps the planepointed due north for the entire flight.

1.) (3 points) Relative to the ground, in which direction is theplane flying (use theta for angles: θ)? Derive an algebraicsolution and then give a numerical answer (three significantfigures is fine) expressed in degrees relative to due north (e.g.’45.0° west of north’).

2.) (2 pts) After flying for 3.0 hours, how far is the planefrom Seattle? Again, derive an algebraic solution, then give thenumerical result (3 significant figures). A smarter pilot is flyingthe next scheduled flight and takes note of the first pilot’sfailure to deal with the winds. He takes the wind speed anddirection into account so that the path of this plane relative tothe ground is due north. This pilot’s plane is identical to thefirst in every way including the speed, and the wind has notchanged in velocity or direction.

3.) (2 pts) How long, in hours, does it take the second pilot toreach Seattle? Again, give the algebraic solution first and then anumerical answer to three significant figures.

4.) (3 pts) Assume the two planes left at the same exact moment.Write an algebraic expression for the distance between two planesas a function of time (∆P(t) = … ). You may only use the variablesVP , VW , θ and t as needed.

Hi I just wanted to double check to see if my answers werecorrect and how you approached the problem. Thanks!