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A 42.0-kg projectile is fired at an angle of 30.0° above the horizontal with an initial speed of 122 m/s from the top of a cliff 154 m above level ground, where the ground is taken to be \(y = 0\). What is the initial total mechanical energy of the projectile?

Answer :

Final answer:

The total initial mechanical energy of the projectile is found by summing the initial kinetic energy (approx. 317172 Joules) and potential energy (approx. 63144 Joules) resulting in approximately 380316 Joules.

Explanation:

The student's question pertains to calculating the initial total mechanical energy of a projectile. In physics, the total mechanical energy of a system in the absence of friction or air resistance (like in this case) is the sum of its kinetic energy and potential energy. The kinetic energy (KE) can be found using the formula KE=1/2mv², where m is the mass and v is velocity. Here, the initial speed of the projectile is given as 122 m/s and the mass is 42 kg.

Substituting these values, you will find that the initial kinetic energy is approximately 317172 Joules.

The potential energy (PE) can be calculated using the formula PE=mgh, where m is mass, g is the acceleration due to gravity (approximately 9.8 m/s² on Earth), and h is height. Here, the cliff's height is 154 m. Substituting these values will determine the potential energy as approximately 63144 Joules.

Finally, by adding both the initial kinetic and potential energy, the total mechanical energy of the projectile can be found, which is approximately 380316 Joules.

Learn more about Total Mechanical Energy here:

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