Explanation:
We define force as the product of mass and acceleration.
F = ma
It means that the object has zero net force when it is in rest state or it when it has no acceleration. However in the case of liquids. just like the above mentioned case, the water is at rest but it is still exerting a pressure on the walls of the swimming pool. That pressure exerted by the liquids in their rest state is known as hydro static force.
Given Data:
Width of the pool = w = 50 ft
length of the pool = l= 100 ft
Depth of the shallow end = h(s) = 4 ft
Depth of the deep end = h(d) = 10 ft.
weight density = ρg = 62.5 lb/ft
Solution:
a) Force on a shallow end:



b) Force on deep end:



c) Force on one of the sides:
As it is mentioned in the question that the bottom of the swimming pool is an inclined plane so sum of the forces on the rectangular part and triangular part will give us the force on one of the sides of the pool.
1) Force on the Rectangular part:




2) Force on the triangular part:

here
h = h(d) - h(s)
h = 10-4
h = 6ft



now add both of these forces,
F = 25000lb + 150000lb
F = 175000lb
d) Force on the bottom:



The astronaut final velocity is 0.06 m/s to the right
Explanation:
In absence of external forces, the total momentum of the box-astronaut system is conserved.
At the beginnig, the total momentum of the two is zero, since they are at rest:

While the final momentum, after the astronaut throws the box, is:

where
m = 11 kg is the mass of the box
M = 79 kg is the mass of the astronaut
v = -0.45 m/s (to the left) is the velocity of the box (we take left as negative direction)
V is the final velocity of the astronaut
The total momentum is conserved, so

And solving , we find V:

And the positive sign indicates that the direction is to the right.
Learn more about momentum:
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They farmed it and got rid of most of the buffalo. They also caused the locust plague from turning up the eggs in the dirt when it was first plowed.
Electric potential energy, or Electrostatic potential energy, is a potential energy that results from conservative Coulomb forces and is associated with the configuration of a particular set of point charges within a defined system.