Video Transcript
Two aircraft fly along the paths
shown, each flying at the same speed. Which color arrow shows the path of
the aircraft that flies between its initial and final positions at the greater
velocity? Is it (A) the blue arrow, (B) the
green arrow, or (C) the velocities are the same?
If the two aircraft have the same
speeds, it means that the plane with the blue arrow, aircraft one, takes more time
to get to its final position than the plane with the green arrow, aircraft two. That’s because the distance flown
by aircraft one shown in the diagram as 𝑑 one is greater than the distance flown by
aircraft two shown in the diagram as 𝑑 two. Aircraft two travels directly to
the final destination. And 𝑑 two can be thought of as the
hypotenuse of the right triangle, where the other sides of the triangle sum together
at the same distance traveled by aircraft one, or 𝑑 one.
According to the equation for
speed, speed is equal to distance divided by time. And if the distance traveled is
greater but the speed is the same, then the time to get to the final destination
must be greater as well. If we look carefully, we can see
that the start and end positions of the two aircraft are equal horizontal distances
from each other and equal vertical distances from each other. For both aircraft, the end
positions are above and to the right of the start positions. This tells us that the
displacements of the two planes are equal, both in magnitude and in direction. We see then that when considering
the start and end positions of the two planes, the directions of the velocities must
be the same.
However, we know that the distance
traveled by aircraft one is greater than that for aircraft two and that the time
taken to arrive at the final destination is greater for the blue path. If we divide the same displacement
by a longer time, it gives a lower velocity. We can say that the velocity 𝑣 one
for the blue line 𝑑 one is less than the velocity 𝑣 two for the green line 𝑑
two. In other words, aircraft two
traveling the green line has greater velocity than aircraft one traveling the blue
line. So the correct answer is option
(B).
