Answer:
v = 14.5 m/s
Explanation:
The Principle Of Conservation Of Mechanical Energy
In the absence of friction, the total mechanical energy is conserved. That means that
Em=U+K is constant, being U the potential energy and K the kinetic energy
U=mgh
[tex]\displaystyle K=\frac{mv^2}{2}[/tex]
The ball with a mass of m=0.8 kg is thrown straight upward from the zero height reference (h=0) and with some speed (v). The potential energy is zero, but the kinetic speed is given by the equation above.
When the ball reaches its maximum height of h=10.7 m, the speed is zero and all the initial kinetic energy was transformed into potential energy, thus:
[tex]\displaystyle \frac{mv^2}{2}=mgh[/tex]
Simplifying by m:
[tex]\displaystyle \frac{v^2}{2}=gh[/tex]
Solving for v:
[tex]\displaystyle v=\sqrt{2gh}[/tex]
Substituting:
[tex]\displaystyle v=\sqrt{2*9.8*10.7}[/tex]
Calculating:
v = 14.5 m/s
