Answer:
294 J
Step-by-step explanation:
To find the kinetic energy (KE) of a 3.00 kg toy falling from a height of 10.0 m, we'll use the kinetic energy formula: KE = 0.5 * m * v^2, where 'm' is the mass of the toy, and 'v' is its velocity.
We'll also apply the conservation of energy principle, which states that the total energy of an isolated system remains constant. This means that the gravitational potential energy (PE) of the toy at the initial height is equal to its kinetic energy just before hitting the ground.
The formula for gravitational potential energy is PE = m * g * h, where 'm' is the mass of the object, 'g' is the acceleration due to gravity, and 'h' is the height of the object.
So, we can equate these two expressions and solve for 'v':
0.5 * m * v^2 = m * g * h
v^2 = 2 * g * h
v = √(2 * g * h)
Plugging in the given values:
v = √(2 * 9.8 m/s² * 10.0 m)
v ≈ 14.0 m/s
Now that we have the velocity of the toy, we can calculate its kinetic energy using the KE formula:
KE = 0.5 * m * v^2
KE = 0.5 * 3.00 kg * (14.0 m/s)^2
KE ≈ 294 J
So, just before hitting the ground, the kinetic energy of the toy is approximately 294 joules.