Answer and Explanation:
The ball is bouncing to a height of 1/3 of its previous height this is a type of geometric sequence the total distance can be found by the sum of geometric sequence
For example let the initial height is 243 fit
After one bounce it will reach 243/3 =81 feet
After second bounce 81/3=27 feet
After third bounce 27/3 =9 feet
After fourth bounce 9/3 =3 feet
So a sequence is formed that is 243,81,27,9,3..........
Here 
Sum of infinite GP = 
From this formula we can find the total distance traveled by the ball
The kinetic energy is
.
Explanation:
The kinetic energy of an object is given by

where
K is the kinetic energy of the object
m is the mass of the object
v is the speed of the object
For the comet in this problem, we have:
is its mass
is the speed
First, we convert the speed from km/h to m/s:

Therefore, the kinetic energy of the comet is

Learn more about kinetic energy here:
brainly.com/question/6536722
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Compression is above the equilibrium and rarefaction is below