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# M5.4.16

Uses vectors and simple operations on vectors (e.g., addition, subtraction, scalar multiplication, dot product) to solve real-world problems.

### Why Is There a Tidal Bulge Opposite the Moon?

Demonstrate and calculate the reasons for tidal bulges of water on both hemispheres of Earth, due to the Moon.

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### Who Hits Harder: The Nordic Skier or Aerial Jumper?

Computer modeling is used to estimate physical quantities that are difficult to measure, in this case, the landing shock experienced by ski jumpers. The landing shock is difficult to measure because attaching instruments to the skiers would affect their balance and possibly cause them to fall or reduce their performance. Using basic principals of physics, the flight trajectories of two forms of competitive ski jumping, Freestyle Aerialist and Nordic Jumpers, were modeled and the landing shocks compared.

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### What the Doppler Effect Tells Us About Distant Stars and Planets

Police officers, air traffic controllers, and astronomers all use the Doppler Effect to determine the speed of an object as it approaches or recedes from their radars or telescopes. The frequency (or pitch, for sound) of waves coming from a moving object is changed an amount directly proportional to the speed of approach or recession. The effect of the change, to raise or lower the frequency, specifically indicates that the source is approaching or receding, respectively.

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