Hello!
The answer is: 8.62m
Why?
There are involved two types of mechanical energy: kinetic energy and potential energy, in two different moments.
First moment:
Before the ball is thrown, where the potential energy is 0.
Second moment:
After the ball is thrown, at its maximum height, the Kinetic Energy turns to 0 (since at maximum height,the speed is equal to 0) and the PE turns to its max value.
Therefore,
[tex]E=PE+KE[/tex]
Where:
[tex]PE=m.g.h[/tex]
[tex]KE=\frac{1*m*v^{2}}{2}[/tex]
E is the total energy
PE is the potential energy
KE is the kinetic energy
m is the mass of the object
g is the gravitational acceleration
h is the reached height of the object
v is the velocity of the object
Since the total energy is always constant, according to the Law of Conservation of Energy, we can write the following equation:
[tex]KE_{1}+PE_{1}=KE_{2}+PE_{2}[/tex]
Remember, at the first moment the PE is equal to 0 since there is not height, and at the second moment, the KE is equal to 0 since the velocity at maximum height is 0.
[tex]\frac{1*m*v^{2}}{2}+m.g.(0)=\frac{1*m*0^{2}}{2}+m.g.h\\\frac{1*m*v_{1} ^{2}}{2}=m*g*h_{2}[/tex]
So,
[tex]h_{2}=\frac{1*m*v_{1} ^{2}}{2*m*g}\\h_{2}=\frac{1*v_{1} ^{2}}{2g}=\frac{(\frac{13m}{s})^{2} }{2*\frac{9.8m}{s^{2}}}\\h_{2}=8.62m}[/tex]
Hence,
The height at the second moment (maximum height) is 8.62m
Have a nice day!
