Answer:
To determine the change in kinetic energy of the object as it falls from a height of 10.0 meters to 5.00 meters, we can use the equation KE = 1/2 mv^2, where KE is the kinetic energy, m is the mass of the object, and v is the velocity. We can also use the equation for gravitational potential energy, which is PE = mgh, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height above the ground.
We know that the potential energy of the object at a height of 10.0 meters is 196 joules, so we can use this information to solve for the mass of the object:
196 = m * 9.80 * 10.0
196 = 98.0m
m = 2.00 kg
We can then use this value for the mass to find the kinetic energy of the object as it falls from a height of 10.0 meters to 5.00 meters:
KE = 1/2 * 2.00 * v^2
KE = 1/2 * 2.00 * (2gh)^2
KE = 1/2 * 2.00 * (2 * 9.80 * 5.00)^2
KE = 196 joules
Thus, the object gains 196 joules of kinetic energy as it falls from a height of 10.0 meters to 5.00 meters.
