I need help with the very last of a series of questions:
The potential energy stored in the compressed spring of a dart gun, with a spring constant of 66.00 N/m, is 0.76 J. Find by how much is the spring is compressed.
My correct answer: 0.152 m
A 0.190 kg dart is fired straight up. Find the vertical distance the dart travels from its position when the spring is compressed to its highest position.
MCA: 0.408 m
The same dart is now fired horizontally from a height of 4.10 m. The dart remains in contact until the spring reaches its equilibrium position. Find the horizontal velocity of the dart at that time.
MCA: 2.83 m/s
Find the horizontal distance from the equilibrium position at which the dart hits the ground.
The Attempt at a Solution
I have no idea how to solve this last question. I thought for a moment that I would use potential energies to find something I could plug into a kinematics equation, but the height up and down would be the same, negating mgh, there is no spring involved at this point, negating (1/2)kx^2, and the mass and horizontal velocity do not change.
Any suggestions on how to proceed?