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Answer :
Final answer:
The dart reaches a height of 2.52 meters when shot straight up.
Explanation:
The height reached by the dart can be determined using the principles of potential and kinetic energy. When the dart is loaded, the spring stores potential energy which is then converted into kinetic energy when the dart is shot. The maximum height can be found by equating the potential energy at maximum height to the initial kinetic energy:
PE = KE
1/2kx^2 = mgh
where PE is potential energy, KE is kinetic energy, k is the spring constant, x is the compression of the spring, m is the mass of the dart, g is the acceleration due to gravity, and h is the maximum height. Rearranging the equation and substituting the given values:
h = (1/2)(185 N/m)(0.0520 m)^2 / (0.0100 kg)(9.8 m/s^2) = 2.52 m
Therefore, the dart reaches a height of 2.52 meters.
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