# A ball with a mass of #350 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #9 (kg)/s^2# and was compressed by #7/4 m# when the ball was released. How high will the ball go?

The height is

The spring constant is

The compression is

The potential energy is

This potential energy will be converted to kinetic energy when the spring is released and to potential energy of the ball

Let the height of the ball be

The acceleration due to gravity is

Then ,

The potential energy of the ball is

Mass of the ball is

The height is

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To find the maximum height the ball will reach, you can use the conservation of mechanical energy. The potential energy stored in the compressed spring is converted into kinetic energy as the ball is launched upwards. At the maximum height, all kinetic energy is converted back into potential energy. You can use the equation for potential energy to find the height.

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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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