Answer:
d = 11.1 m
Explanation:
Since the inclined plane is frictionless, this is just a simple application of the conservation law of energy:
![\frac{1}{2} m {v}^{2} = mgh](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20m%20%7Bv%7D%5E%7B2%7D%20%20%3D%20mgh)
Let d be the displacement along the inclined plane. Note that the height h in terms of d and the angle is as follows:
![\sin(15) = \frac{h}{d} \\ or \: h = d \sin(15)](https://tex.z-dn.net/?f=%20%5Csin%2815%29%20%20%3D%20%20%5Cfrac%7Bh%7D%7Bd%7D%20%20%5C%5C%20or%20%5C%3A%20h%20%3D%20d%20%5Csin%2815%29%20)
Plugging this into the energy conservation equation and cancelling m, we get
![{v}^{2} = 2gd \sin(15)](https://tex.z-dn.net/?f=%20%7Bv%7D%5E%7B2%7D%20%20%3D%202gd%20%5Csin%2815%29)
Solving for d,
![d = \frac{ {v}^{2} }{2g \sin(15) } = \frac{ {(7.5 \: \frac{m}{s}) }^{2} }{2(9.8 \: \frac{m}{ {s}^{2} })(0.259)} \\ = 11.1 \: m](https://tex.z-dn.net/?f=d%20%3D%20%20%5Cfrac%7B%20%7Bv%7D%5E%7B2%7D%20%7D%7B2g%20%5Csin%2815%29%20%7D%20%20%3D%20%20%5Cfrac%7B%20%7B%287.5%20%5C%3A%20%20%5Cfrac%7Bm%7D%7Bs%7D%29%20%7D%5E%7B2%7D%20%7D%7B2%289.8%20%5C%3A%20%20%5Cfrac%7Bm%7D%7B%20%7Bs%7D%5E%7B2%7D%20%7D%29%280.259%29%7D%20%20%20%5C%5C%20%3D%2011.1%20%5C%3A%20m)
<span>The correct frequency when you tune a guitar is
when you hear the right tune in your own hearing and standard. The measure
frequency of a guitar string is when you measure the tune of the string
correctly. This is not the same because manual tuning is affected by many
factors.</span>
Answer:
![U=5*10^7ft.Ib](https://tex.z-dn.net/?f=U%3D5%2A10%5E7ft.Ib)
Explanation:
From the question we are told that
Weight ![W= 10000bs](https://tex.z-dn.net/?f=W%3D%2010000bs)
Altitude ![H=5000ft](https://tex.z-dn.net/?f=H%3D5000ft)
Speed ![V=125kts\\1kts=0.514m/s\\V=125*0.514=>64.25m/s](https://tex.z-dn.net/?f=V%3D125kts%5C%5C1kts%3D0.514m%2Fs%5C%5CV%3D125%2A0.514%3D%3E64.25m%2Fs)
Generally the equation for Potential energy ids mathematically given as
![Potential\ Energy\ U=mgh](https://tex.z-dn.net/?f=Potential%5C%20Energy%5C%20U%3Dmgh)
![U=Wh](https://tex.z-dn.net/?f=U%3DWh)
![U=10000*5000](https://tex.z-dn.net/?f=U%3D10000%2A5000)
![U=5*10^7ft.Ib](https://tex.z-dn.net/?f=U%3D5%2A10%5E7ft.Ib)