[quote]From : http://www.physics.umd.edu/lecdem/outreach/QOTW/arch1/q002.htm
Identical balls are launched at the same time with the same velocity from the left front end of the two-track gizmo photographed below. (Because this is a physics problem, there is no friction.) A race of the balls will then ensue. The ball on the flat track clearly proceeds across the track at a constant speed. The ball on the dipped track goes for a while at that same speed, goes faster while it is in the dipped part of the track, then returns to its original speed for the final segment of the track. Note that it also travels further.
[img]http://www.physics.umd.edu/lecdem/outreach/QOTW/pics/c2-11.gif[/img]
What will happen?

* (a) The ball on the straight track will reach the end first.
* (b) The ball on the track with the dip will reach the end first.
* (c) The race will end in a tie.
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Click

The answer is (b); the ball on the dipped track gets to the end first and wins the race. The two balls go along together for the first part of the race. As the ball on the dipped track goes down, its horizontal velocity increases, so it gets ahead. When it returns to its original level, it slows down to its original horizontal speed, but in so doing it never goes slower than the ball on the flat track, so it never gets behind the other ball or even allows the flat track ball to catch up. The two balls then move along at the same speed with the dipped track ball remaining ahead of the straight track ball by a constant amount.

Click on the photograph of the apparatus above for a video showing this demonstration in action.

The same thing happens when two people are walking along a straight flat road. If one of the two runs for a short time (the dip) then slows down to the original walking speed, the runner will get ahead during the time he or she is running. After slowing back down to the same walking speed, the two will then move along at the same speed but the one who ran will remain a constant distance ahead of the person who walked the whole time.

A more mathematical way of "discovering" this result is to draw graphs of horizontal velocity versus time for each of the two balls. Then draw curves of the integral of the velocity curves for each, which are the horizontal position versus time for each of the balls. After the ball on the dipped track returns to its original level its horizontal position can be observed from the graph to be greater than that of the ball on the flat track for any time.
or play with the following simulation to find out answer.

When the two balls are launched from one end of the track with the same initial velocity, what will happen:
1) the ball #1 on the straight track arrives at the other end first
2) the ball #2 on the track with the dip arrives at the other end first
3) the race is a tie - both balls reach the other end at the same time?
This is a java version for one of our physics demostration. Think about it, select the answer to active the program.
Did you get the correct answer?

Press the start button to restart.

1. Click the left button within the window will suspend the animation

1. click it again to resume.
2. Clcik the right mouse button and drag it up and down

1. to change the shape of the lower track.

4. Shape of the track ( from left to right)

1. section 1 red curve: part of a circle (1/4)
tangential component of the gravitation field is the source of the acceleration.

section 2 blue curve: Trajectory for a projectile

(with initial velocity when it entering this region)
So, horizontal component of the velocity is a constant.

section 3 red curve: part of a circle.
The solpe for the curves match at the boundary.
particle will accelerate (as section 1) but with different acceleration

sectin 4 blue curve: Trajectory for projectile similar similar to section 2
section 5 green line: horizontal line.
The velocity is a constant in this region.

5. The horizontal component of the velocities are also shown.

This applet was originated from one of the demonstrations developed by Prof. Berg (Dept. of physics at Maryland, College Park) many years ago.