Posted by LILY on .
Two planes fly from toronto to
philadelphia. Plane a flies via pittsburgh whereas passenger on plane B have a direct flight. Pittsburgh is 350km due south of Toronto and 390km due west of Philadelphia. The airspeed of both planes is 400km/h and a steady wind is blowing from the east at 60km/h
a) What direction must the pilot point the plane flying from toronto to pittsburgh?
b) How long will the entire flight take for plane A assuming a 0.50-h layover in pittsburgh?
c) How mich time must the pilot of plane B wait before leaving toronto if she is to arrive in philadelphia at the same time plane A arrives?
(wat i really need is how to draw the diagram for the first question and how to get started for the rest of the questions and i can take it from there)
a) The "airspeed" vector has a magnitude of 400 km/h and a direction in which the pilot points the plane (which is what they are asking you to calculate). The wind velocity vector has magnitude 60 km/h and direction TOWARD the west. The ground velocity vector of the plane going to Piitsburgh has a direction due south. It is the sum of the airspeed and windspeed vectors. You have two sides and one angle of the vector-addition triangle, so can solve for all unknowns.
b) Get the ground speed of the Pittsburhg leg of the trip from the vector triangle opf the last problem. Divide 350 km by that speed for the elapsed time. For the leg of the trip to Philly, the ground speed is just 400 - 60 = 340 km/h. Compute the elapsed time for that leg, and add the first leg elapsed time plus 0.5 hours.
c) Compute the travel time for the direct flight using the same method to get the ground velocity vector. You know its direction already. Compare that to the answer in (b) to get the required waiting time before takeoff.