Respuesta :
Given gravitational potential energy when he's lifted is 2058 J.
Kinetic energy is transferred to the person.
Amount of kinetic energy the person has is -2058 J
velocity of person = 7.67 m/s².
Explanation:
Given:
Weight of person = 70 kg
Lifted height = 3 m
1. Gravitational potential energy of a lifted person is equal to the work done.
[tex]PE_g=W=m\times g\times h\\Acceleration due to gravity = g = 9.8 \ m/s^2 \\PE_g= m = m\times g\times h= 70\times 9.8 \times 3 = 2058\ kg.m/s^2 = 2058\ J[/tex]
Gravitational potential energy is equal to 2058 Joules.
2. The Gravitational potential energy is converted into kinetic energy. Kinetic energy is being transferred to the person.
3. Kinetic energy gained = Potential energy lost = [tex]-PE_g = -2058\ kg.m/s^2[/tex]
Kinetic energy gained by the person = (-2058 kg.m/s²)
4. Velocity = ?
Kinetic energy magnitude= [tex]\frac{1}{2} m\times v^2 = m\times g \times h[/tex]
Solving for v, we get
[tex]v=\sqrt{2gh} =\sqrt{2\times 9.8 \times 3} = \sqrt{58.8} = 7.67 m/s^2[/tex]
The person will be going at a speed of 7.67 m/s².
