# A ball with a mass of #650 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 #3/5 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 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

Then ,

The potential energy of the ball is

The mass of the ball is

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To find the maximum height the ball will reach, you can use the principle of conservation of mechanical energy. The potential energy stored in the compressed spring is converted into kinetic energy when released, and then into potential energy at the maximum height.

Using the formula for potential energy stored in a spring (U = \frac{1}{2} kx^2) (where (k) is the spring constant and (x) is the compression distance), you can find the potential energy stored in the spring.

(U = \frac{1}{2} \times 16 \times (3/5)^2)

Next, equate this potential energy to the potential energy at maximum height using the formula (U = mgh), where (m) is the mass of the ball, (g) is the acceleration due to gravity (approximately (9.8 m/s^2)), and (h) is the maximum height.

Solve for (h).

(h = \frac{U}{mg})

Substitute the values and calculate (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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