# A ball with a mass of #40 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #16 (kg)/s^2# and was compressed by #2/5 m# when the ball was released. How high will the ball go?

The height reached by the ball is

The spring constant is

The compression of the spring is

The potential energy stored in the spring 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 reached by the ball is

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The height the ball will reach can be calculated using the conservation of energy. The potential energy stored in the compressed spring is converted into the gravitational potential energy of the ball at its highest point.

The potential energy stored in the spring (Us) is given by Hooke's Law: Us = (1/2)kx^2, where k is the spring constant and x is the compression distance.

The gravitational potential energy at the maximum height (Ug) is given by Ug = mgh, where m is the mass of the ball, g is the acceleration due to gravity, and h is the height.

Setting these equal and solving for h: (1/2)kx^2 = mgh

h = (k/m) * x^2/g

Substitute the given values: h = (16 / (0.04)) * (2/5)^2 / 9.8

Calculate to find the height h.

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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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