Question

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 if its total mechanical energy is 41.70 J? Round to the nearest tenth. m

Answer 1

Answer:

The correct answer to the following question will be "2.7 m".

Explanation:

The given values are:

Velocity, v = 16 m/s

mass, m = 0.27 kg

Mechanical energy, M.E = 41.70 J

g = 9.8 m/s²

As we know,

Kinetic energy, $K=\frac{mv^2}{2}$

Potential energy, $U=m.g.h$

Now, the total mechanical energy will be:

⇒  $\frac{mv^2}{2}+U$

⇒  $41,71 \ kg.m^2/s^2$

Now,

⇒  $h=\frac{E-(\frac{mv^2}{2})}{mg}$

On putting the estimated values, we get

⇒    $=\frac{41.70-(\frac{0.27(16)^2}{2})}{0.27\times 9.8}$

⇒    $=\frac{41.70-(\frac{0.27\times 256}{2} )}{2.64}$

⇒    $=\frac{41.70-34.56}{2.64}$

⇒    $=\frac{7.14}{2.64}$

⇒    $=2.7 \ m$