A ball is tossed into the air with an initial velocity of 5.0 m/s from an initial height of 20.0 m. If the ball has a mass of 1.2 kg, what is the total initial energy of this system? Assume the gravitational field constant, g, is 9.8 N/kg.
To calculate the total initial energy, we need to consider both the potential energy and the kinetic energy.
The potential energy (PE) of an object at a given height is given by the formula PE = mgh, where m is the mass (1.2 kg), g is the gravitational field constant (9.8 N/kg), and h is the height (20.0 m). Plugging in the values, we get:
PE = (1.2 kg) * (9.8 N/kg) * (20.0 m)
PE = 235.2 J
The kinetic energy (KE) of an object in motion is given by the formula KE = (1/2)mv^2, where m is the mass (1.2 kg) and v is the velocity (5.0 m/s). Plugging in the values, we get:
KE = (1/2) * (1.2 kg) * (5.0 m/s)^2
KE = 15 J
Therefore, the total initial energy of the system is the sum of the potential energy and the kinetic energy:
Total initial energy = PE + KE
Total initial energy = 235.2 J + 15 J
Total initial energy = 250.2 J
So, the total initial energy of the system is 250.2 Joules.