Answer:
a) 1.67 m/s
b) 23kJ
Explanation:
We need to apply the linear momentum conservation formula, that states:
![m1*v_{o1}+m2*v_{o2}=m1*v_{f1}+m2*v_{f2}](https://tex.z-dn.net/?f=m1%2Av_%7Bo1%7D%2Bm2%2Av_%7Bo2%7D%3Dm1%2Av_%7Bf1%7D%2Bm2%2Av_%7Bf2%7D)
in this case:
![3.45*10^4kg*2.60m/s+2*3.45*10^4kg*1.20m/s=3*m1*v_{f}\\v_f=1.67m/s](https://tex.z-dn.net/?f=3.45%2A10%5E4kg%2A2.60m%2Fs%2B2%2A3.45%2A10%5E4kg%2A1.20m%2Fs%3D3%2Am1%2Av_%7Bf%7D%5C%5Cv_f%3D1.67m%2Fs)
the initital kinetic energy is:
![K_i=\frac{1}{2}*3.45*10^4kg*(2.60m/s)^2+2(\frac{1}{2}*3.45*10^4kg*(1.20m/s)^2\\K_i=167kJ](https://tex.z-dn.net/?f=K_i%3D%5Cfrac%7B1%7D%7B2%7D%2A3.45%2A10%5E4kg%2A%282.60m%2Fs%29%5E2%2B2%28%5Cfrac%7B1%7D%7B2%7D%2A3.45%2A10%5E4kg%2A%281.20m%2Fs%29%5E2%5C%5CK_i%3D167kJ)
and the final:
![K_f=3*\frac{1}{2}*3.45*10^4kg*(1.67m/s)^2\\K_f=144kJ](https://tex.z-dn.net/?f=K_f%3D3%2A%5Cfrac%7B1%7D%7B2%7D%2A3.45%2A10%5E4kg%2A%281.67m%2Fs%29%5E2%5C%5CK_f%3D144kJ)
The energy lost is given by:
![E_l=|K_f-K_i|\\E_l=23kJ](https://tex.z-dn.net/?f=E_l%3D%7CK_f-K_i%7C%5C%5CE_l%3D23kJ)
I have no Idea it might be 5cm squared
Answer:
![f_{ecco} = 360 Hz](https://tex.z-dn.net/?f=f_%7Becco%7D%20%20%3D%20360%20Hz)
Explanation:
The change of frecuency of sound due to the movement of the source is colled Doppler Effect.
As James (the source) is running toward the wall, the frecuency reaching the wall (so the eco sound) will be higher than the source. In this case the frecuency at the wall will be:
![f_{2} = f_{1} (\frac{v}{v-v_{s} } )](https://tex.z-dn.net/?f=f_%7B2%7D%20%20%3D%20f_%7B1%7D%20%20%28%5Cfrac%7Bv%7D%7Bv-v_%7Bs%7D%20%7D%20%29)
where
is the speed of source, 2 m/s
and
is the speed of sound, given that we have wind movind the air in the opposite direction respect to the wall, the speed of sound would be:
Replacing the values: ![f_{2} = 357 Hz](https://tex.z-dn.net/?f=f_%7B2%7D%20%20%3D%20357%20Hz)
Now the wall becames the new source, and James (the observer is aproaching the source), for an observer aproaching the source the new frecuency will be:
![f_{3} = f_{2} (1 + \frac{v_{s}}{v} )](https://tex.z-dn.net/?f=f_%7B3%7D%20%20%3D%20f_%7B2%7D%20%20%281%20%2B%20%5Cfrac%7Bv_%7Bs%7D%7D%7Bv%7D%20%29)
Now the waves are traveling in the direction of wind, so the velocity of sound will be:
Replacing:
![f_{3} = 360 Hz](https://tex.z-dn.net/?f=f_%7B3%7D%20%20%3D%20360%20Hz)
Option A, B, C, D
Child on a swing, Pendulum, Bow and Arrow, Roller Coaster is mechanical energy being conserved
<u>Explanation:</u>
Mechanical energy is the total of kinetic and potential energy in a thing that is employed to do a job. A conservative force is a power like gravitation or a spring that “bends backward” energy that was conveyed by producing activity. The friction and other non conservative forces, nevertheless, conservation of mechanical energy is surely conserved.
When one stretches or contracts an elastic object, one does act fronting the spring force, and that task finishes up saved as elastic potential energy. Constantly shifting things up and down, producing variations in potential energy is termed as gravitational potential energy.
Here Child on a swing, Pendulum, Bow & Arrow, Roller Coaster in all there is the continuous conversion between gravitational/elastic potential energy and kinetic energy.