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I have a two-part problem to solve. I think I solved it but in the class the professor told us that there's something wrong with the exercise.

The spring constant of a toy dart gun is 1350 N/m. To cock the gun the spring is compressed 1 cm (0.01 m). The 5g (0.005 kg) dart, fired straight upward, reaches a maximum height of 24 m. g is 9.81 m/s^2. Determine the energy dissipated by air friction during the dart's ascent.

My solution:

E = -1/2 *(k) *(x)^2 + m*g*h

=-0.5*1350* (0.01)^2 + 0.005*9.8*24

= -0.0675 + 1.176 = 1.1085 J

Part 2.

What speed should the projectile have when it returns to its starting point?

Solution: m*g*h = 0.5*m*v^2

v = sqrt(2*g*h)

=sqrt(470.4) = 21.69 m/s

These make sense to me, but i don't know why the professor told me there's something wrong in the problems.

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# Homework Help: Conservation of energy of a dart gun

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