Answer:
Step-by-step explanation:
To find the velocity and height of the object when its kinetic energy is equal to its potential energy, we can use the principle of conservation of mechanical energy.
1. Potential energy (PE) is given by the formula: PE = m * g * h
- m is the mass of the object (which we don't have in this question)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- h is the height of the object (500 m in this case)
2. Kinetic energy (KE) is given by the formula: KE = (1/2) * m * v^2
- v is the velocity of the object
3. Since the kinetic energy is equal to the potential energy, we can set up the equation:
(1/2) * m * v^2 = m * g * h
4. We can cancel out the mass (m) on both sides of the equation.
5. Solving for v, we get:
v^2 = 2 * g * h
6. Plugging in the values:
v^2 = 2 * 9.8 m/s^2 * 500 m
7. Simplifying:
v^2 = 9800 m^2/s^2
8. Taking the square root of both sides, we get:
v = √(9800 m^2/s^2)
Therefore, the velocity of the object when its kinetic energy is equal to its potential energy is approximately 99.0 m/s. However, we cannot determine the exact height of the object without knowing its mass.