To determine the velocity with which the object hits the ground, we can use the principles of conservation of energy. The potential energy of the object at the initial height is converted into kinetic energy as it falls. We can equate these energies to find the final velocity.
The potential energy (PE) of an object at a certain height is given by the formula:
PE = m * g * h
Where: m = mass of the object (2 kg) g = acceleration due to gravity (approximately 9.8 m/s²) h = height (5 m)
Substituting the values:
PE = 2 kg * 9.8 m/s² * 5 m = 98 J
The kinetic energy (KE) of the object when it hits the ground is given by the formula:
KE = 0.5 * m * v²
Where: m = mass of the object (2 kg) v = final velocity (to be determined)
Equating the potential energy to the kinetic energy:
PE = KE 98 J = 0.5 * 2 kg * v²
Simplifying:
98 J = v²
Taking the square root of both sides:
√(98 J) = √(v²) 9.899 m/s = v
Therefore, the object hits the ground with a velocity of approximately 9.899 m/s.