Answer:
C. 590 mph

Explanation:
Given:
- velocity of jet,

- direction of velocity of jet, east relative to the ground
- velocity of Cessna,

- direction of velocity of Cessna, 60° north of west
Taking the x-axis alignment towards east and hence we have the velocity vector of the jet as reference.
Refer the attached schematic.
So,

&


Now the vector of relative velocity of Cessna with respect to jet:



Now the magnitude of this velocity:

is the relative velocity of Cessna with respect to the jet.
Answer:
(a) The ratio of the pressure amplitude of the waves is 43.21
(b) The ratio of the intensities of the waves is 0.000535
Explanation:
Given;
density of gas,
= 2.27 kg/m³
density of liquid,
= 972 kg/m³
speed of sound in gas,
= 376 m/s
speed of sound in liquid,
= 1640 m/s
The of the sound wave is given by;

Where;
is the pressure amplitude

(b) when the pressure amplitudes are equal, the ratio of the intensities is given as;

Answer:
h = 50.49 m
Explanation:
Data provided:
Speed of skier, u = 2.0 m/s
Maximum safe speed of the skier, v = 30.0 m/s
Mass of the skier, m = 85.0
Total work = 4000 J
Height from the starting gate = h
Now, from the law of conservation of energy
Total energy at the gate = total energy at the time maximum speed is reached

where, g is the acceleration due to the gravity
on substituting the values, we get

or
170 + 833.85 × h = 4000 + 38250
or
h = 50.49 m
Answer:
The heat capacity for the second process is 15 J/K.
Explanation:
Given that,
Work = 100 J
Change temperature = 5 k
For adiabatic process,
The heat energy always same.


We need to calculate the number of moles and specific heat
Using formula of heat


Put the value into the formula


We need to calculate the heat
Using formula of heat

Put the value into the formula


We need to calculate the heat capacity for the second process
Using formula of heat

Put the value into the formula



Hence, The heat capacity for the second process is 15 J/K.