Quick Math

Here are eight deceptively easy math problems.  Can you solve them in your head?




Spherical Excess

If the interior angles of a spherical triangle add up to 252 degrees, what fraction of the sphere's surface is inside the triangle?

Answer: 1/10th

How fast must you drive?

You have a thirty mile commute to work that you normally drive at sixty mph.  If you start out ten minutes late, how fast do you have to drive to get to work on time?


Answer


How many pavers?

You want to make a path using 12” X 12” pavers with 2” spaces between them.

How many pavers do you need for a 28 foot path?


Answer


How high is the moon?

It is December and the Sun is at 20 degrees south declination.  There is a full Moon.  In Boulder, Colorado, (40 N latitude) what is the elevation angle of the Moon at midnight?



Double the angle off the bow.

You are sailing on a southerly course at ten knots off the coast of San Diego, CA.  You observe the Point Loma Lighthouse twenty degrees off the port bow.  After holding course and speed constant for thirty minutes, the lighthouse is now forty degrees off the port bow.  How far are you now from the lighthouse?


Sink rate for a stable approach.

Your approach ground speed is one hundred knots and you want to maintain a three degree glide slope.  What should your vertical speed be in feet per minute? (Use Pi = 3, and 1 NM = 6000 ft.)


Answer

Electron velocity from an electric field.


Given that the ground state hydrogen electron has a kinetic energy of 13.6 eV, and a velocity of 1/137 th the speed of light; what is the velocity of an electron after being accelerated by a 54.4 Volt electric field?  (Hint: 54.4/13.6 = 4)



Tensile force from a swinging weight.


A one pound weight is attached to a string.  If it is being swung in a horizontal circle so that the string sweeps a cone with an apex angle of 120 degrees, what is the tension in the string?