To determine the velocity at which the body hits the ground, we can use the principle of conservation of energy. The potential energy of the body at the initial height is converted into kinetic energy at the moment it reaches the ground.
The potential energy (PE) of an object at a certain height is given by the equation:
PE = m * g * h
where m is the mass of the object (2 kg), g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height (5 m).
PE = 2 kg * 9.8 m/s² * 5 m = 98 J
The kinetic energy (KE) of an object is given by the equation:
KE = (1/2) * m * v²
where v is the velocity of the object.
Since the potential energy is fully converted into kinetic energy at the moment the body hits the ground, we can equate the potential energy to the kinetic energy:
PE = KE
98 J = (1/2) * 2 kg * v²
Simplifying the equation:
98 J = v²
Taking the square root of both sides:
v = sqrt(98 J)
Calculating the value:
v ≈ 9.90 m/s
Therefore, the body will hit the ground with a velocity of approximately 9.90 m/s.