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Resolving Vectors into Axial Components

Identify perpendicular components of vectors

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Physics Behind Darts

Physics Behind Darts

Credit: PeterPan23
Source: http://en.wikipedia.org/wiki/File:Darts_in_a_dartboard.jpg
License: CC BY-NC 3.0

The game of darts as we know it has been played for over 100 years since it was created in 1896. To play the game, participants throw small pointed spears known as darts at a numbered circular object. Considered by some as a game of chance, it was soon elevated to a game of skill after being challenged in court. The game of darts is really based on physics and not on chance.

Amazing But True!

  • According to the World Darts Federation, the distance between a competitor and the dartboard should be 2.37 meters. If you were to release the dart at the same height as the bulls-eye and assume an average throwing speed of 17.9 m/s, you can calculate how much the dart will drop before it hits the dartboard.

\begin{align*}x = 2.37 \ m ; v_{\circ ,x} &= 17.9 \ m/s \\ \text{time of flight}= t &= \frac{x}{v_{\circ ,x}} = 0.13 \ s \\ y = 0+\frac{1}{2} \ at^2 &= 0.08 \ m\end{align*}

  • If the bulls-eye has a diameter of 0.012 m, you would have to aim slightly above the bulls-eye to score a perfect shot. It is important to note that the slower your throw is, the higher you will have to aim the dart to account for the amount of time the dart will be under the influence of gravity.

Show What You Have Learned

Using the information provided above, answer the following questions.

  1. What force mainly affects the vertical drop in the dart?
  2. Explain why the air resistance is considered negligible in this case.
  3. If you had to release the dart at the center of the bulls-eye, what could you do to ensure that the effects due to gravity would be negligible and that you would hit your target?

Image Attributions

  1. [1]^ Credit: PeterPan23; Source: http://en.wikipedia.org/wiki/File:Darts_in_a_dartboard.jpg; License: CC BY-NC 3.0

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