Final answer:
The initial total mechanical energy of a projectile system is calculated by adding its kinetic energy, derived from its mass and velocity, to its potential energy, which depends on its mass and height above a reference point.
Step-by-step explanation:
The question is asking for the initial total mechanical energy of a projectile system. To calculate this, we need to consider both the kinetic and potential energy of the projectile at the moment it is launched. The kinetic energy (KE) can be found using the formula KE = 0.5 × m × v^2, where m is the mass of the object and v is the speed. The potential energy (PE) due to gravity is given by PE = m × g × h, where g is the acceleration due to gravity (9.8 m/s^2) and h is the height above the reference point. For a projectile fired at an angle, only the horizontal component of the velocity contributes to the kinetic energy.
To find the initial total mechanical energy, we add the kinetic and potential energy together: Total Mechanical Energy = KE + PE.
To solve the given problem:
- Calculate the kinetic energy: KE = 0.5 × 44.0 kg × (134 m/s)^2
- Calculate the potential energy: PE = 44.0 kg × 9.8 m/s^2 × 150 m
- Add KE and PE to find the total mechanical energy.
By doing these calculations, we can find which option (A, B, C, or D) correctly represents the initial total mechanical energy of the system.