**Explanation:**
There is a distinction between asking about the final speed and asking about
the time of travel. As explained in Section 6.6 when discussing amusement
park rides, the only factor affecting the final speed is the change in height.
Since the vertical displacement is the same, we know that both balls will
have the same final speed.
However, to find the time of travel we will focus on the horizontal component
of the velocity. The displacement along the horizontal d_{H} is
related to the average velocity along the horizontal v_{H} and time
*t* by: d_{H} = v_{H} t
The ball with the larger average horizontal velocity arrives first. As shown
in the velocity time graph made by the applet, the first ball accelerates
for a short time then moves at a constant velocity. Except for a small region,
the horizontal component of the velocity of the second ball is similar to
the first. However, in the region of the path drawn in red, ball 2 accelerates
beyond the maximum value reached by ball 1 then slows down to reach the
final speed. Since the second ball never moves slower than the first,
we can deduce that its average velocity along the horizontal is greater.
Thus, it arrives first. |