To calculate the velocity with which the body hits the ground, we can use the principle of conservation of energy. Initially, the body possesses potential energy due to its height, and upon reaching the ground, this potential energy is converted into kinetic energy.
The potential energy (PE) of an object at a certain height is given by the formula:
PE = m * g * h
where m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s² on Earth), and h is the height.
In this case, the potential energy at the height of 5m is:
PE = 2 kg * 9.8 m/s² * 5 m = 98 J
According to the law of conservation of energy, this potential energy is converted into kinetic energy when the body hits the ground. The kinetic energy (KE) of an object is given by the formula:
KE = (1/2) * m * v²
where v is the velocity of the object.
Equating the potential energy to the kinetic energy, we can solve for the velocity:
PE = KE
98 J = (1/2) * 2 kg * v²
98 J = v²
v² = 98 J
v ≈ √98 J
v ≈ 9.90 m/s
Therefore, the body will hit the ground with a velocity of approximately 9.90 m/s.