An airplane flies from point A to point B,a distance of 100 km,and back again with an airspeed of 250 km/h.What is the difference in the time for this round trip on a day when a wind of speed 50.0 km/h blows from A toward B and on a day when a wind of speed 50.0 km/h blows in a direction perpendicular to AB?
A)zero
B)1.0 min
C)5.5 min
D)4.5 min
E)10 min

Question

Quizplus · Accepted Answer

Let's use the formula for time: time = distance / speed

- On the day when there is a headwind of 50 km/h (blowing from A to B), the airplane's groundspeed (air speed - wind speed) will be 250 km/h - 50 km/h = 200 km/h. Using time = distance / speed, we get:

time going from A to B = 100 km / 200 km/h = 0.5 h = 30 min
time going from B to A = 100 km / 200 km/h = 0.5 h = 30 min
Total time for round trip = 30 min + 30 min = 60 min

- On the day when there is a crosswind of 50 km/h (blowing perpendicularly to AB), the airplane's groundspeed will still be 200 km/h (we assume the wind does not affect the time it takes to fly in the perpendicular direction). Using the same formula, we get:

time going from A to B = 100 km / 200 km/h = 0.5 h = 30 min
time going from B to A = 100 km / 200 km/h = 0.5 h = 30 min
Total time for round trip = 30 min + 30 min = 60 min

Therefore, the difference in time for the round trip is zero. The answer is D.

An Airplane Flies from Point a to Point B,a Distance