Question

What is the height of the volleyball above the gym floor when its total mechanical energy is 41.70 J? Round to the nearest tenth.

Answer 1

The height of the voleyball ball is equal to 2.69m.

Why?

It seems that you forgot to write some information about the problem, so, to help you, I will try to complete the statement of the problem.

The complete statement would be "Elias serves a volleyball at a velocity of 16 m/s. The mass of the volleyball is 0.27 kg.What is the height of the volleyball above the gym floor when its total mechanical energy is 41.70 J? Round to the nearest number."

Now, we can solve the problem by using the Law of Conservation of Energy.

Then, calculating we have:

$KE=\frac{1}{2}*m*v^{2}\\\\PE=mgh$

$TotalME=KE+PE\\\\TotalME=\frac{1}{2}*0.27kg*(16\frac{m}{s})^{2}+0.27kg*9.81\frac{m}{s^{2}}*h\\\\41.70J=0.135kg*256\frac{m^{2} }{s^{2}}+2.648\frac{kg.m}{s^{2}}*h\\\\41.70J=34.56J.+2.648\frac{kg.m}{s^{2}}*h\\\\41.70J-34.56J=2.648\frac{kg.m}{s^{2}}*h\\\\7.14\frac{kg.m^{2} }{s^{2}}=2.648\frac{kg.m}{s^{2}}*h\\\\h=\frac{7.14\frac{kg.m^{2} }{s^{2}}}{2.648\frac{kg.m}{s^{2}}}=2.69m$

Hence, we have that the height of the voleyball ball is equal to 2.69m.

Have a nice day!