Final answer:
The speed of a 10-kg brick dropped from 15 meters when it reaches a height of 6 meters is calculated using the conservation of energy. The difference in potential energy at the start and at 6 meters gives the kinetic energy, which is used to solve for the velocity.
Step-by-step explanation:
To determine the speed of a 10-kg brick when it is dropped from rest from a height of 15 meters and reaches 6 meters in height, we can use the principle of conservation of energy. Initially, the brick has potential energy and no kinetic energy. As it falls, the potential energy decreases, and kinetic energy increases, keeping the total energy constant.
The potential energy (PE) at the start is given by PE = mgh, where m is the mass, g is the acceleration due to gravity (9.81 m/s2), and h is the height. At the initial height of 15 meters, the PE is PEinitial = 10 kg * 9.81 m/s2 * 15 m. When the brick reaches 6 meters, its PE is PEfinal = 10 kg * 9.81 m/s2 * 6 m.
The kinetic energy (KE) the brick has at 6 meters can be found by KE = PEinitial - PEfinal. We then use KE = 0.5 * m * v2 to solve for the velocity (v). After calculating and taking the square root, we round the velocity to the nearest hundredth (0.01).
Using the given method, we compute the brick's speed at 6 meters, ensuring the answer is precise and informative.