(Geometry) Are We Congruent?

I tutor a high school student, and a problem similar to this showed up on his homework. See if you can figure it out - I thought it was fun to solve.

A Quick Primer - What Does Congruent Mean Again?

Why, I'm glad you asked Holmes. Here's a review.

Is there enough information provided to prove that the two triangles in the shape above are congruent?

  • Yup
  • Nope!
  • A, B, C...eaaasy as 1, 2, 3...

Use latex to write equations.

Betting on the Bullseyes

You and your friends are hanging out at a bar after work shooting darts. One of your friends seems to hit the bull's eye every 3 out of 4 darts. You and your group of friends decide to bet among each other whether he'll hit 2 bull's eyes in the next 3 three shots.

Should you bet that he will? 



Rocketing in space

A rocket in outer space has its engines on and is ejecting fuel at 6000 ft/s in the opposite direction with respect to the rocket. If the rocket is burning fuel at a rate of 80 lbs/s, what is its thrust?

(Electronics - Medium) Voltage Across an Inductor

Inductors are energy storage elements like capacitors, except that they induce voltage. (The purple lines in the diagram to the side are magnetic field lines produced by the inductor at a single moment in time)

With the change of current through the coiled wire of an inductor, a magnetic field is produced, one which creates a surrounding voltage. In the presence of a DC current, the inductor acts just like a short circuit. But in an AC circuit, the inductor induces a voltage that is proportional to the derivative of the changing current.

This property is thanks to Faraday's law, one of Maxwell's equations (Originally discovered/described by Faraday, and then collected and unified by Maxwell, hence the two names). One way of stating Farady's law is :

"The induced electromotive force in any closed circuit is equal to the negative of the time rate of change of the magnetic flux enclosed by the circuit" (thanks Wikipedia).

The changing magnetic field produces a curling electric field; since we curled a wire (the inductor itself) around the magnetic field running through the center of the inductor, this curling electric field induces a voltage in the circuit.

Given the following equation for the current running through an air-filled inductor, what is the voltage drop across the inductor? Checking the spec sheet for the inductor you purchased, you find it has a length of 1 cm, a coil radius of 5 mm, and 100 million turns.  Fortunately, someone already did the calculation for you at the end of the spec sheet, and wrote down "$L = 1$", whatever that means.

Use latex to write equations.

(Fluid Mechanics - Medium) What's Coming Out Of That Storage Tank??

You've got a pressurized, closed cylindrical storage tank that you partially filled with blood...(or maybe it's just wine). Anywho, the tank has a 10 m diameter, and the liquid has a specific gravity of 0.9.

The absolute pressure in the tank above the liquid is 200 kPa. On a whim, you decide to open the 50 cm nozzle which is located at a height of 50 cm . When the blood (or wine) initially starts pouring out, what is the fluid jet's initial velocity?

  • 11.3 m/s
  • 18.0 m/s
  • 18.6 m/s
  • 23.9 m/s

Use latex to write equations.