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annabelx4

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## Homework Statement

Learning Goal: To apply the law of conservation of energy to an object launched upward in the gravitational field of the earth.

In the absence of nonconservative forces such as friction and air resistance, the total mechanical energy in a closed system is conserved. This is one particular case of the law of conservation of energy.

In this problem, you will apply the law of conservation of energy to different objects launched from the earth. The energy transformations that take place involve the object's kinetic energy and its gravitational potential energy . The law of conservation of energy for such cases implies that the sum of the object's kinetic energy and potential energy does not change with time. This idea can be expressed by the equation

K_i + U_1 + W_other = K_2 + U_2 ,

where "i" denotes the "initial" moment and "f" denotes the "final" moment. Since any two moments will work, the choice of the moments to consider is, technically, up to you. That choice, though, is usually suggested by the question posed in the problem.

What is the speed of the object at the height of ?

Express your answer in terms of and . Use three significant figures in the numeric coefficient.

## Homework Equations

K_i + U_1 + W_other = K_2 + U_2

## The Attempt at a Solution

(1/2) mv^2 + 0 + 0 = (1/2) mv^2 + mg (v^2 / 4g)

so when I solve for v it = 0

mv^2 = 2(0)

v = 0

What did I do wrong?