# Work and Energy - The law of conservation of energy

Problem Statement:

An airplane flies at a height h = 1000 m with a constant speed vA = 200 km / h. The pilot drops a bomb from the plane. Determine the speed of the bomb when it reaches the ground if we neglect the friction of the air.

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Solution:

We are going to solve this problem by applying the energy conservation principle. First, we represent the physical situation described in the problem in the following figure.

As you can see in the figure, we use the lowest point of the trajectory of the bomb as the origin of heights to determine its potential energy.

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When solving a problem using the energy conservation principle, we must first define what are the initial and final states of the body in motion. Then we identify the forces acting on the body to determine whether its mechanical energy is conserved or not between these two states.

We will use the bomb at point A as the initial state (see figure). It corresponds to the moment when the airplane drops the bomb. The final state will be the bomb at point B when it touches the ground.

The only force acting during the motion of the bomb is its weight, which is a conservative force, so the mechanical energy of the bomb is conserved between states A and B:

The height of point A is h, the altitude of the airplane. The bomb is dropped with an initial speed vA (which coincides with the speed of the airplane). When it reaches point B its height is zero.

Therefore:

In the problem we have used g = 10 m/s2

Before substituting givens you must convert them to SI units.

Do not forget to include the units in the results of the problems.

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