(Physics - Medium) Spring-loaded Toy Dart Gun

A spring-loaded toy dart gun is used to shoot a dart straight up in the air. The dart reaches a maximum height hmax. Afterwards, the same dart is shot straight up a second time from the same gun, but this time the spring is compressed only half as far before firing. Neglecting friction and assuming an ideal spring...

How far up does the dart go this time?

(Physics - Easy) Work While You Work

While working out, you pick up a 10 kg weight from rest on the ground and lift it to a height of 2 meters above the ground and hold it there at rest. Assume $ g = 10 m/s^{2} $ .

How much work do you do on the weight in moving it?

(Math - Medium) The Trouble With Tribbles...Exponential Growth

Uh-oh. You're a starship captain returning back to your ship from a well-needed leave, and your first mate's just informed you that there's been a Tribble outbreak. (Tribbles are cute, furry little things that multiply magnitudes faster than rabbits.)

The first Tribble was brought on-board 3 days ago, and it only takes one of them to tango (translation: breed). In the first 12 hours, the original Tribble gave birth to 10 Tribbles. Assuming exponential growth, about how many of these things are now on your ship?


      72
      1339
      1,771,561
      8,561,283

(Calculus - Easy) Zorbing Down a Hill

It's snowing, and instead of sulking indoors all winter, you and your friend decide to roll with the weather...literally. You grab a Zorb Human Hamster Ball (as reviewed by Mr. George Takei), and line the ball surface with a material that attracts snow. You flip a coin over who gets to go first, and into the ball you squeeze.

Down a hill you go! The radius of you - human-sized snowball that starts at 1.5 m - is increasing at a rate of 0.3 meters/minute . How fast is your volume increasing when your diameter is 5 m?

  • 0.3 meters cubed per minute
  • 6.5 meters cubed per minute
  • 18 meters cubed per minute
  •  24 meters cubed per minute
  • Ooo, look, people! *change course*

Use latex to write equations.


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(Fluid Mechanics - Medium) Laminar or Turbulent Flow

The 20 m long steel pipe below has a 25mm inner diameter. It carries water at a rate of 4.5 m3/h. The density of water is 1000 kg/m3, and water has an absolute viscosity of 1.00 x 10-3 Pa*s.

Would the flow in the pipe be considered laminar, in transition or turbulent?

  • laminar
  • in transition
  • turbulent
  • I want honey

Use latex to write equations.


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