Answer:
Part a) When collision is perfectly inelastic

Part b) When collision is perfectly elastic

Explanation:
Part a)
As we know that collision is perfectly inelastic
so here we will have

so we have

now we know that in order to complete the circle we will have


now we have

Part b)
Now we know that collision is perfectly elastic
so we will have

now we have


Answer:
The overall velocity of the water when it hits the bottom is:

Explanation:
Use the law of conservation of energy.
Call it instant [1] to the moment when the water is just before reaching the falls.
At this moment its height h is 206 meters and its velocity horizontally
is
m/s.
At the instant [1] the water has gravitational power energy 

The water also has kinetic energy Ek.

Then the Total E1 energy is:

In the instant [2] the water is within an instant of touching the ground. At this point it only has kinetic energy, since the height h = 0. However at time [2] the water has maximum final velocity 
So:

As the energy is conserved then 

Now we solve for
.

Answer: L.M = 34.69
Area of the bar = 25835m^2
Explanation: To design a bar that can withstand temperature at 773K for 10years, we need to calculate and know:
1) the Larson Miller value
2) rupture time
3) creep rate
4) stress and load.
Please find the attached file for the solution