A spring-loaded toy gun is used to shoot a ball of mass m= 1.50\; \rm{kg} straight up in the air, as shown in the figure. View Figure The spring has spring constant k = 667\;\rm{N/m}. If the spring is compressed a distance of 25.0 centimeters from its equilibrium position y=0 and then released, the ball reaches a maximum height h_max (measured from the equilibrium position of the spring). There is no air resistance, and the ball never touches the inside of the gun. Assume that all movement occurs in a straight line up and down along the y axis.

I believe the question you copied wasn't complete. I believe it finishes:


Find the muzzle velocity of the ball (i.e. the velocity of the ball at the spring's equilibrium position y=0).

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I suggest you take a look at Calculating Muzzle Velocity (http://en.wikipedia.org/wiki/Muzzle_energy) via Wikipedia and try to figure this problem out before asking for help.

Actually I think the question is probaably to find h_max.

Here's a hint: use conservation of energy principles. When the spring is compressed a distance x it's potential energy is (1/2)kx^2, where x is the deflection of the spring from equilibrium. When it's released all that potential energy is converted to kinetic energy as the mass shoots upward. Then that kinetic energy is converted to potential energy against the earth's gravitational field as the mass climbs to its maximum height - that potential energy is equal to mgh. So set (1/2) kx^2 = mgh, and solve for h.