7. A 2000.0 kg boulder sits on the top of a 50.0 m cliff. As the boulder rolls off, it loses 3.0% of its mechanical energy as heat. How much heat energy goes the boulder lose? How much mechanical energy does the boulder have right before hits the ground?

please answer if you know this cause i need this for my homework due tomorow and im doing badly in physics

To calculate the heat energy lost by the boulder and the mechanical energy it has right before hitting the ground, we need to follow a few steps.

Step 1: Calculate the potential energy of the boulder when it is at the top of the cliff.
The potential energy is given by the formula PE = mgh, where m is the mass (2000.0 kg), g is the acceleration due to gravity (9.8 m/s²), and h is the height (50.0 m). So:
PE = 2000.0 kg * 9.8 m/s² * 50.0 m = 980,000 J

Step 2: Calculate the amount of potential energy lost as it rolls off the cliff.
Given that the boulder loses 3.0% of its mechanical energy as heat, we need to determine the mechanical energy that is converted to heat. The mechanical energy is equal to the initial potential energy, so:
Heat energy = 3.0% * 980,000 J = 0.03 * 980,000 J = 29,400 J

Step 3: Calculate the mechanical energy the boulder has right before hitting the ground.
The mechanical energy is the sum of the potential energy and the kinetic energy (KE) right before hitting the ground. The KE is given by the formula KE = 0.5 * m * v², where v is the final velocity (unknown at this point). Since the boulder falls freely, the potential energy is converted to kinetic energy and there is no further loss. So:
Mechanical energy = PE + KE = PE + 0.5 * m * v²

Now, to calculate v (the final velocity) before hitting the ground, we can use the conservation of energy principle. The potential energy lost is equal to the kinetic energy gained:
PE_lost = KE_gained

Substituting the values:
29,400 J = 0.5 * 2000.0 kg * v²

Solving for v:
v² = (29,400 J) / (0.5 * 2000.0 kg) = 29.4 J/kg
v = √(29.4 J/kg) = 5.42 m/s

Finally, substitute the value of v into the expression for mechanical energy:
Mechanical energy = 980,000 J + 0.5 * 2000.0 kg * (5.42 m/s)² = 980,000 J + 0.5 * 2000.0 kg * 29.4 J/kg
Mechanical energy = 980,000 J + 29,400 J = 1,009,400 J

Therefore, the boulder loses 29,400 J of heat energy and has 1,009,400 J of mechanical energy right before hitting the ground.