# A ball with a mass of #256 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #36 (kg)/s^2# and was compressed by #12/4 m# when the ball was released. How high will the ball go?

The maximum altitude of the ball is

This can be solved using energy conservation,

When the ball reaches its maximum altitude, all of the kinetic energy has been transformed into gravitational potential energy as the ball momentarily comes to a stop before falling back toward the earth. In other words, all of the spring potential energy stored in the spring initially is converted into gravitational potential energy stored in the ball at its maximum altitude. This gives us:

Hope that helps!

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The ball will go up to a height of 0.8 meters.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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