Answer:
The maximum possible speed is 4.85 m/s.
Explanation:
The Principle Of Conservation Of Mechanical Energy
In the absence of friction, the total mechanical energy is conserved. It means that
:
[tex]E_m=U+K[/tex] is constant, being U the potential energy and K the kinetic energy
U=mgh
Where m is the mass of the object, g is the gravitational acceleration and h is the height from a fixed reference.
[tex]\displaystyle K=\frac{mv^2}{2}[/tex]
Where v is the speed.
When the person is at a maximum height of 2 meters, the speed is 0. Thus the mechanical energy is made only of potential energy.
Let's fix the reference for the height to the point where the person is at minimum height (1 m from the ground level). The maximum height with respect to this reference is h=2.2 m - 1 m = 1.2 m.
The potential energy is:
U = m*9.8*1.2
U = 11.76m
When the person is at the minimum (zero) height, the mechanical energy is made only of kinetic energy. Since the mechanical energy is conserved, then:
[tex]\displaystyle \frac{mv^2}{2}=11.76m[/tex]
Multiplying by 2 and simplifying by m:
[tex]v^2=2*11.76=23.52[/tex]
Solving for v:
[tex]v=\sqrt{23.52}=4.85[/tex]
[tex]\boxed{v=4.85}[/tex]
The maximum possible speed is 4.85 m/s.
