-- The table tennis ball bounces back with virtually its entire original speed.
-- The bowling ball rolls forward, so slowly that only complex expensive laboratory equipment can detect and measure its speed.
-- Once again, momentum is conserved !
The image of the water tower and the houses is in the attachment.
Answer: (a) P = 245kPa;
(b) P = 173.5 kPa
Explanation: <u>Gauge</u> <u>pressure</u> is the pressure relative to the atmospheric pressure and it is only dependent of the height of the liquid in the container.
The pressure is calculated as: P = hρg
where
ρ is the density of the liquid, in this case, water, which is ρ = 1000kg/m³;
When it is full the reservoir contains 5.25×10⁵ kg. So, knowing the density, you know the volume:
ρ = 
V = ρ/m
V = 
V = 525 m³
To know the height of the spherical reservoir, its diameter is needed and to determine it, find the radius:
V = 
![r = \sqrt[3]{ \frac{3}{4\pi } .V}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%5B3%5D%7B%20%5Cfrac%7B3%7D%7B4%5Cpi%20%7D%20.V%7D)
r = ![\sqrt[3]{\frac{525.3}{4\pi } }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cfrac%7B525.3%7D%7B4%5Cpi%20%7D%20%7D)
r = 5.005 m
diameter = 2*r = 10.01m
(a) Height for House A:
h = 15 + 10.01
h = 25.01
P = hρg
P = 25.01.10³.9.8
P = 245.10³ Pa or 245kPa
(b) h = 25 - 7.3
h = 17.71
P = hρg
P = 17.71.1000.9.8
P = 173.5.10³ Pa or 173.5 kPa
b). The power depends on the RATE at which work is done.
Power = (Work or Energy) / (time)
So to calculate it, you have to know how much work is done AND how much time that takes.
In part (a), you calculated the amount of work it takes to lift the car from the ground to Point-A. But the question doesn't tell us anywhere how much time that takes. So there's NO WAY to calculate the power needed to do it.
The more power is used, the faster the car is lifted. The less power is used, the slower the car creeps up the first hill. If the people in the car have a lot of time to sit and wait, the car can be dragged from the ground up to Point-A with a very very very small power ... you could do it with a hamster on a treadmill. That would just take a long time, but it could be done if the power is small enough.
Without knowing the time, we can't calculate the power.
...
d). Kinetic energy = (1/2) · (mass) · (speed squared)
On the way up, the car stops when it reaches point-A.
On the way down, the car leaves point-A from "rest".
WHILE it's at point-A, it has <u><em>no speed</em></u>. So it has no (<em>zero</em>) kinetic energy.
