Explanation:
a) The height of the ball h with respect to the reference line is
![h = L - L\cos{31°} = L(1 - \cos{31°})](https://tex.z-dn.net/?f=h%20%3D%20L%20-%20L%5Ccos%7B31%C2%B0%7D%20%3D%20L%281%20-%20%5Ccos%7B31%C2%B0%7D%29)
so its initial gravitational potential energy
is
![U = mgh = mgL(1 - \cos{31°})](https://tex.z-dn.net/?f=U%20%3D%20mgh%20%3D%20mgL%281%20-%20%5Ccos%7B31%C2%B0%7D%29)
![\:\:\:\:\:=(0.25\:\text{kg})(9.8\:\text{m/s}^2)(0.65\:\text{m})(1 - \cos{31})](https://tex.z-dn.net/?f=%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%3D%280.25%5C%3A%5Ctext%7Bkg%7D%29%289.8%5C%3A%5Ctext%7Bm%2Fs%7D%5E2%29%280.65%5C%3A%5Ctext%7Bm%7D%29%281%20-%20%5Ccos%7B31%7D%29)
![\:\:\:\:\:=0.23\:\text{J}](https://tex.z-dn.net/?f=%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%3D0.23%5C%3A%5Ctext%7BJ%7D)
b) To find the speed of the ball at the reference point, let's use the conservation law of energy:
![\Delta{K} + \Delta{U} = 0 \Rightarrow K_0 + U_0 = K + U](https://tex.z-dn.net/?f=%5CDelta%7BK%7D%20%2B%20%5CDelta%7BU%7D%20%3D%200%20%5CRightarrow%20K_0%20%2B%20U_0%20%3D%20K%20%2B%20U)
We know that the initial kinetic energy
as well as its final gravitational potential energy
are zero so we can write the conservation law as
![mgL(1 - \cos{31°}) = \frac{1}{2}mv^2](https://tex.z-dn.net/?f=mgL%281%20-%20%5Ccos%7B31%C2%B0%7D%29%20%3D%20%5Cfrac%7B1%7D%7B2%7Dmv%5E2)
Note that the mass gets cancelled out and then we solve for the velocity v as
![v = \sqrt{2gL(1 - \cos{31°})}](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7B2gL%281%20-%20%5Ccos%7B31%C2%B0%7D%29%7D)
![\:\:\:\:\:= \sqrt{2(9.8\:\text{m/s}^2)(0.65\:\text{m})(1 - \cos{31°})}](https://tex.z-dn.net/?f=%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%3D%20%5Csqrt%7B2%289.8%5C%3A%5Ctext%7Bm%2Fs%7D%5E2%29%280.65%5C%3A%5Ctext%7Bm%7D%29%281%20-%20%5Ccos%7B31%C2%B0%7D%29%7D)
![\:\:\:\:\:= 1.3\:\text{m/s}](https://tex.z-dn.net/?f=%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%3D%201.3%5C%3A%5Ctext%7Bm%2Fs%7D)
Indicate valleys, hills, steepness and gentleness of slopes.
Answer: The pressure in a liquid dec reaches with depth. F
The pressure in a liquid increases with depth.
The upthrust on an object is larger when it is deeper in a pool. 7
The bottom of a dam is thinner than the top of a dam. F
The bottom of a dam is thicker than the top of a dam.
The pressure is bigger at the bottom of a lake because of the weight of water above it. 7
I think these are the answers.
The kinetic energy and gravitational potential energy changes during its movement from ground to the top height.
<h3>What happens to kinetic and potential energy while motion?</h3>
When the ball moves upward, its gravitational potential energy is increases and kinetic energy begins to decrease but when the ball falls towards the earth, its gravitational potential energy is transformed into kinetic energy. When the ball collides with the ground, the kinetic energy is transformed into other forms of energy.
Learn more about kinetic energy here: brainly.com/question/20658056
Answer & Explanation: Waste management are all activities and actions required to manage waste from its inception to its final disposal. There are several methods of managing waste with its strengths and weaknesses. The strengths include;
* It creates employment
* It keeps the environment clean
* The practice is highly lucrative
* It saves the earth and conserves energy
The weaknesses of the methods of waste management includes;
* The sites are often dangerous
* The process is mostly
* There is a need for global buy-in
* The resultant product had a short life