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A 9.5 kg test rocket is fired vertically from Cape Canaveral. Its fuel gives it a kinetic energy of 1915 J by the time the rocket engine burns all of the fuel. What additional height will the rocket rise? Assume that air resistance is negligible.

Question

A 9.5 kg test rocket is fired vertically from Cape Canaveral. Its fuel gives it a kinetic energy of 1915 J by the time the rocket engine burns all of the fuel. What additional height will the rocket rise? Assume that air resistance is negligible.

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Solution

To solve this problem, we need to use the principle of conservation of energy. The kinetic energy (KE) that the rocket has when its fuel is burned out will be converted into potential energy (PE) as it continues to rise.

The formula for kinetic energy is KE = 1/2 * m * v^2, where m is the mass and v is the velocity.

The formula for potential energy is PE = m * g * h, where m is the mass, g is the gravity constant (9.8 m/s^2 on Earth), and h is the height.

We know that the kinetic energy is 1915 J and the mass of the rocket is 9.5 kg. We can set the kinetic energy equal to the potential energy and solve for the height:

1915 J = 9.5 kg * 9.8 m/s^2 * h

Solving for h gives:

h = 1915 J / (9.5 kg * 9.8 m/s^2) = 20.5 m

So, the rocket will rise an additional 20.5 meters.

This problem has been solved

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