(Math) Ever Try Bungee Jumping?

Bungee jumping may seem like a reckless activity to some, but in truth, many commercial bungee operators rigorously ensure their equipment conforms to industry standards and guidelines. Operators commonly double and triple check the calculations and fittings before every jump.

As an operator, you need to determine the appropriate rope length, which may differ from person to person, day to day (weather conditions), and rope to rope ("stretchiness").

To prevent whiplash, injuries (and a subsequent lawsuit), bungee operators typically aim for the rope to elongate to an additional 300% (i.e. x4 normal length) for a softer fall.

If your 5'5" 145 lb girlfriend/boyfriend/malamut wants to jump and just barely glance a 47m lake below, what length should you spec the rope to be?

Stuck? Click here for a hint!
      6.5 m
      8.25 m
      11.35 m
(The founder Jen Tran actually jumped from the lake pictured above in the video.)

The Power of Compound Interest (Economics Pt 1 of 2)

Aunt Bessie 

Aunt Bessie 

You ever hear those stories about someone’s “Aunt Bessie”?  We’ve all heard em in some way…  She was a kind, old woman that lived dirt poor her entire life. Yet after her passing, you (and the entire town) are stunned to discover that Aunt Bessie actually died a…. MULTI- MILLIONAIRE!

So how’d the old woman do it? It turns out Aunt Bessie understood the timeless wisdom of Continual Saving + Compound Interest.

Taking a cue from Aunt Bessie, one day you decide to invest your savings of $10,000. After thorough research, you choose a semi-conservative Mutual Fund that yields approximately 6% per year (not bad!). The fund also “compounds” its returns quarterly—meaning it pays out and automatically reinvests its profits every single quarter. After 10 years in this fund, your single investment of $10,000 would grow into how much money total (approximate)?

(Hint: Remember a 6% annual return implies a 1.5% quarterly return)

      A) $16,000
      B) $17,500
      C) $18,000
      D) $20,500

Radiant Heat From a Lighting System

A hydroponic lighting system radiates out 1500W of heat energy in a large room. The lighting system has an emissivity of 0.62 and temperature of 87°C. What steady-state temperature will this lighting system heat up the room to?

      A) 410K

      B) 380K

      C) 360K

(Electrical) Lighting the Christmas Tree

Every year it's your job to light the Christmas tree... and you have to wire it up too!

The lights are separated into sections. Each section consists of 16 light bulbs connected in series. Each light bulb is rated at 1.5V 0.07A, and they need 24V power supply. However this year you can't find the right spare bulbs. Instead you get some rated at 2.4V 0.07A.

If you connect 2.4V 0.07A and 1.5V 0.07A bulbs together in series, what happens?

(Physics) Block Attached to Spring on Incline

A block of mass m is attached to a relaxed spring on an inclined plane. The 
block is allowed to slide down the incline, and comes to rest. The coefficient of kinetic 
friction of the block on the incline is µk. For which definition of the system is the change 
in total energy (after the block is released) zero?