Physics Help!?

Question

a jetliner can fly 6.5 hours on a full load of fuel. Without any wind, it flies at a speed of 2.10 x 10^2 m/s. the plane is to make a round-trip by heading due west for a certain distance, turning around, and then heading due east for the return trip. during the whole flight, the plane encounter 55.0 m/s wind from the jet stream, which blows from west to east. what is the maximum distance that the plane can travel due west and just be able to return home?





A swimmer, capable of swimming at a speed of 1.3 m/s in still water (the swimmer can swim with a speed of 1.3 m/s relative to the water) starts to swim directly across a 2.2 km wide river. However the current is 0.91 m/s and it carries the swimmer downstream


a) how long does it take the swimmer to cross the river?


b) how far downstream will the swimmer be upon reaching the other side of the river?

Answer 1

Let the maximum distance that the plane can travel due west and just be able to return home to be x m.
Without any wind, the plane flies at a speed of 210 m/s. Thus the real speed due west is (210-55)m/s = 155m/s, and the real speed due east is (210+55)m/s = 265m/s.
x/155 + x/265 = 6.5*3600
or: x = 6.5*3600/(1/155 + 1/265) = 2.29x10^3 km.

Since the directions of the current and the swimming are perpendicular to one another, it takes the swimmer:
2200/1.3 = 1692 (s) = 28 min
to cross the river. But the swimmer will be
0.91*1692 = 1540m = 1.5km
downstream upon reaching the other side of the river.