Neat! They take the same time! Since the problem was ill posed, I guessed a pitch for the ramp of 38 degrees and then generalized.
:-)
Bob at PC
________________________________________
From: Phys-l [phys-l-bounces@phys-l.org] on behalf of John Denker [jsd@av8n.com]
Sent: Saturday, July 27, 2013 1:51 AM
To: Phys-L@Phys-L.org
Subject: [Phys-L] quickest route
On 07/26/2013 07:31 PM, Anthony Lapinski wrote:
... wins since ball has highest acceleration at start.
Consider the right triangle shown here, with vertices
A,B,C facing sides a,b,c respectively.
B
|\
| \
a | \ c
| \
|________\ A
C b
The base b is horizontal and the altitude a is vertical,
aligned with the local gravitational field.
The ball starts at rest at point B. The ball then moves
under the influence of gravity along some path to A. The
only forces are gravity and the forces of constraint. The
question is this: Is it faster for the ball to approximately
follow path BCA, with a reasonably sharp 90 degree turn near
point C, or is it faster to follow the direct path BA?
For simplicity, assume the "sharp" turn is rounded enough
to keep the forces finite, but sharp enough to have no
significant effect on the timing.
This question is well within the scope of the introductory
algebra-based physics course.
And yes, I am quite aware that there is something ill-posed
in the question as I have stated it. Students should learn
to deal with this sort of thing. Some hints can be found at: http://www.av8n.com/physics/ill-posed.htm#sec-how-to