Grade 12 Planes in Air question, help

[IQmissing]

Two planes fly from Toronto to Philadelphia (To. - Philly). Plane A flies via Pittsburgh whereas passengers on plane B have a direct flight. Pitts. is 350km due south of To. and 390km due West of Philly. The airspeed of both planes is 400km/h and a steady wind is blowing from the east at 60.0km/h.

a) what direction must the pilot take for the plane flying from To. to Pitts?

I drew a vector diagram with a line directly south, then a vector to the west connecting it to make a ninety degress angle. The hypoteneuse was the course required, so I found the angle between the hypoteneuse and vector going south using sin(angle) = 60.0km/h divided by 400.0km/h . I got a heading of 400 km/h (9° E of S) sound good?

b) How long will the entire flight take for plane A assuming a 0.50-h layover in Pittsburgh? Don't know how to account for airspeed

Please Help, then question c) How much time must the pilot of plane B wait before leaving Toronto if she is to arrive in Philly at the same time plane A arrives?

Thanks for your help

 

[Valerie Park]

! For part b) the time taken for plane A would be (350 km + 390 km) ÷ 400 km/h = 2.5 h + 0.5 h for the layover = 3 h. For part c) the time the pilot of plane B must wait before leaving Toronto is 3 h - (390 km ÷ 400 km/h) = 2.25 h.

 

[sir-pinski]

a) Yes, your heading of 9° E of S is correct for the plane flying from Toronto to Pittsburgh. This means the pilot should fly in a direction that is 9° east of south to reach Pittsburgh.

b) To calculate the total time for the entire flight for plane A, we need to consider the distance and speed for each segment of the journey. The distance from Toronto to Pittsburgh is 350km and the distance from Pittsburgh to Philadelphia is 390km. The airspeed is 400km/h for both segments. So the total time for the entire flight would be (350km/400km/h) + (390km/400km/h) + 0.50h = 0.875h + 0.975h + 0.50h = 2.35 hours.

c) To arrive at the same time as plane A, plane B would need to make up for the 0.50 hour layover in Pittsburgh. This means the pilot of plane B would need to wait 0.50 hour less than the total flight time of 2.35 hours, which is 1.85 hours. So the pilot of plane B should leave Toronto 1.85 hours after plane A leaves to arrive in Philadelphia at the same time.