Answer:

Explanation:
First, the instant associated to the angular displacement is:

Roots of the second-order polynomial are:

Only the first root is physically reasonable.
The angular velocity is obtained by deriving the angular displacement function:


The angular acceleration is obtained by deriving the previous function:

The resultant linear acceleration on the rim of the disk is:






A = -9.8
v = -9.8t -8
s = -4.9 t2 -8t +25
So… -5t^2 -8t + 25 =0, we’ll rearrange to 5t^2 + 8t - 25. We get two roots, one is positive and is 1.59 seconds
V = -9.8(1.59) - 8 = -23.6
So… it takes 1.59 seconds to hit the ground at -23.6 m/s.
Explanation:
It is given that,
= -40 mi/h,
= -40 mi/h
The negative sign indicates that x and y are decreasing.
We have to find
. Equation for the given variables according to the Pythagoras theorem is as follows.

Now, we will differentiate each side w.r.t 't' as follows.

or, 
So, when x = 4 mi, and y = 3 mi then z = 5 mi.
As, 
= 
= 
= 52
Thus, we can conclude that the cars are approaching at a rate of 52 mi/h.
Answer:
a) The mass flow rate through the nozzle is 0.27 kg/s.
b) The exit area of the nozzle is 23.6 cm².
Explanation:
a) The mass flow rate through the nozzle can be calculated with the following equation:

Where:
: is the initial velocity = 20 m/s
: is the inlet area of the nozzle = 60 cm²
: is the density of entrance = 2.21 kg/m³
Hence, the mass flow rate through the nozzle is 0.27 kg/s.
b) The exit area of the nozzle can be found with the Continuity equation:



Therefore, the exit area of the nozzle is 23.6 cm².
I hope it helps you!