# Josh's physics picks: September 20, 2015

Here are my four picks for this week

The first is an old but very good problem called "Rolling Down the Stairs". Here we have a cylinder rolling down a staircase which of course at first accelerates. Unlike the inclined plane, the staircase imparts some retarding momentum to the cylinder, and at some point this causes the cylinder to enter an oscillation about some mean terminal velocity. Finding this balance point requires some careful thinking, and in the end it is quite a rewarding problem.

The next is "Safe Three Pointer". Here we ask about the smartest angle at which a basketball player can launch a three point shot. He can launch at whatever angle and velocity he picks, but some are going to be less stable choices than others. Finding the optimal angle requires us to balance constraints. The final step can be approached in several ways, either a clever analytic approach or a numerical intersection.

The third choice is "Out for a Hike". Here we examine the tradeoff between packing a backpack full of food and the decreased performance of our hiking. If we pack a small amount of food, we won't be able to hike very far, but we'll be able to do that hiking very efficiently. If we pack a lot of food, we'll be able to hike longer distances, but will be quite inefficient for much of the hike. How far can we go on a given weight of food?

Finally, we end with the classic scenario of a rotating fluid. Whether it be a rotating bucket or stirred coffee, spinning liquids form a stable equilibrium surface. Can you find the right one?

Note by Josh Silverman
5 years, 1 month ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$