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A spring-powered dart gun is mounted vertically. A dart is inserted into the barrel of the gun and pushed down, compressing the (ideal) spring until the trigger is engaged. The trigger is then pulled, releasing the spring, which pushes the dart.

The dart leaves the gun vertically and remains vertical (it does not rotate along any axis) until it reaches its highest point.

The information given is as follows:

  • The mass of the dart is $27\text{ grams}$.
  • The spring was compressed $6.5\text{ cm}$ from its equilibrium position.
  • The spring constant is $410\text{ N/m}$.

What is the maximum height that the dart will achieve (above its original position on the compressed spring)?

A

$3.3\text{ m}$

B

$33\text{ m}$

C

$50\text{ m}$

D

$99\text{ m}$

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