The kinetic energy (KE) of the ball and stone can be calculated using the formula KE = 0.5 * m * v^2, and the height from which they were dropped can be found by equating gravitational potential energy to kinetic energy since energy is conserved.
To answer the student's questions about the ball and the stone dropped from a height, we’ll rely on the principles of gravitational potential energy (GPE), kinetic energy (KE), and the conservation of energy.
Kinetic Energy Calculation
The kinetic energy of an object can be calculated using the formula KE = 0.5 * m * v2, where m is the mass of the object and v is the velocity.
Gravitational Potential Energy and Height Calculation
The gravitational potential energy can be calculated using the formula GPE = m * g * h, where m is the mass, g is the acceleration due to gravity, and h is the height. Since energy is conserved, we can set the GPE at the top equal to the KE at the bottom (just before impact) to solve for h. Because both the ball and stone hit the water at the same speed, we can use the same method for both objects, with the stone's mass being double that of the ball, which would result in the same height from which they were dropped.