Answer:
a). 1.218 m/s
b). R=2.8
Explanation:


Momentum of the motion the first part of the motion have a momentum that is:


The final momentum is the motion before the action so:
a).




b).
kinetic energy

Kinetic energy after

Kinetic energy before

Ratio =

Here we can use momentum conservation as in this type of collision there is no external force on it

now here we can say




now here we can say


now by coefficient of restitution
for elastic collision we know that e = 1


now by solving the two equation


also we know that

so final speed of the nail is 6.875 m/s
To calculate the velocity of the sound wave, we use this formula:
V = 331 + [0.6*T],
Where V is the velocity and T represents temperature.
When the temperature is 36 degree Celsius, we have
V = 331 + [0.6 * 36]
V = 331 + 21.6 = 352.6
Therefore, V = 352.6 m/s.
To explain, I will use the equations for kinetic and potential energy:

<h3>Potential energy </h3>
Potential energy is the potential an object has to move due to gravity. An object can only have potential energy if 1) <u>gravity is present</u> and 2) <u>it is above the ground at height h</u>. If gravity = 0 or height = 0, there is no potential energy. Example:
An object of 5 kg is sitting on a table 5 meters above the ground on earth (g = 9.8 m/s^2). What is the object's gravitational potential energy? <u>(answer: 5*5*9.8 = 245 J</u>)
(gravitational potential energy is potential energy)
<h3>Kinetic energy</h3>
Kinetic energy is the energy of an object has while in motion. An object can only have kinetic energy if the object has a non-zero velocity (it is moving and not stationary). An example:
An object of 5 kg is moving at 5 m/s. What is the object's kinetic energy? (<u>answer: 5*5 = 25 J</u>)
<h3>Kinetic and Potential Energy</h3>
Sometimes, an object can have both kinetic and potential energy. If an object is moving (kinetic energy) and is above the ground (potential), it will have both. To find the total (mechanical) energy, you can add the kinetic and potential energies together. An example:
An object of 5 kg is moving on a 5 meter table at 10 m/s. What is the objects mechanical (total) energy? (<u>answer: KE = .5(5)(10^2) = 250 J; PE = (5)(9.8)(5) = 245 J; total: 245 + 250 = 495 J</u>)
Water because the light is able to enter the water and allow heat to enter faster.