Help with finding position

Question

The Krakow airport is 3 km west and 5 km north of the city center. At 1 pm, Zuza
took off in a Cessna 730. Every six minutes, the plane’s position changed by 9 km east and
7 km north. At 2:30 pm, Zuza was flying over the town of Jozefow. In relation to the center
of Krakow, (a) where is Jozefow? (b) where was Zuza after t hours of flying?

Answer 1

The distance Zuza travels is 9 km east and 7 km north every 6 minutes.

6 minutes is 1/10 of an hour, so the distance he travels is 90t east and 70t north.

 

The airport is 3 km west and 5 km north from Krakow.

You have to calculate the two distances, then add the distance to the airport.

Be careful.  If east is the positive x direction, that 3 km west is really a negative: -3 km.

 

(b) After t hours, Zuza's distance from Krakow is:

90t - 3 km east

70t + 7 km north

 

(a) 2:30 is 1.5 hours after his 1:00 start time, so use t=1.5 and the answer to (b) to calculate the answer.