Answer:2.55 rad/s
Explanation:
Given
Diameter of ride=5 m
radius(r)=2.5 m
Static friction coefficient range=0.60-1
Here Frictional force will balance weight
And limiting frictional force is provided by Centripetal force
![f=\mu N=\mu m\omega ^2\cdot r](https://tex.z-dn.net/?f=f%3D%5Cmu%20N%3D%5Cmu%20m%5Comega%20%5E2%5Ccdot%20r)
weight of object=mg
Equating two
f=mg
![\mu m\omega ^2\cdot r=mg](https://tex.z-dn.net/?f=%5Cmu%20m%5Comega%20%5E2%5Ccdot%20r%3Dmg)
![\omega ^2=\frac{g}{\mu r}](https://tex.z-dn.net/?f=%5Comega%20%5E2%3D%5Cfrac%7Bg%7D%7B%5Cmu%20r%7D)
![\omega =\sqrt{\frac{g}{\mu r}}](https://tex.z-dn.net/?f=%5Comega%20%3D%5Csqrt%7B%5Cfrac%7Bg%7D%7B%5Cmu%20r%7D%7D)
![\omega =2.55 rad/sec](https://tex.z-dn.net/?f=%5Comega%20%3D2.55%20rad%2Fsec)
Answer: The Company has spent $5 million in research and development over the past 12 months developing cutting-edge battery technology which will be incorporated ...
Explanation: uhmmmmmm i dont know this one but it is pretty ez
Let the rescue boat starts at an angle theta with the North
now its velocity towards East is given as
![v_x = 24sin\theta](https://tex.z-dn.net/?f=v_x%20%3D%2024sin%5Ctheta)
![v_y = -24cos\theta + 3](https://tex.z-dn.net/?f=v_y%20%3D%20-24cos%5Ctheta%20%2B%203)
now in some time "t" it will catch the boy
so we will have
![t = \frac{0.5}{24sin\theta}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B0.5%7D%7B24sin%5Ctheta%7D)
also we have
![t = \frac{2}{-24cos\theta + 3}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B2%7D%7B-24cos%5Ctheta%20%2B%203%7D)
now we have
![\frac{2}{-24cos\theta + 3} = \frac{0.5}{24sin\theta}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B-24cos%5Ctheta%20%2B%203%7D%20%3D%20%5Cfrac%7B0.5%7D%7B24sin%5Ctheta%7D)
![4*24sin\theta = - 24cos\theta + 3](https://tex.z-dn.net/?f=4%2A24sin%5Ctheta%20%3D%20-%2024cos%5Ctheta%20%2B%203)
![96 sin\theta + 24cos\theta = 3](https://tex.z-dn.net/?f=96%20sin%5Ctheta%20%2B%2024cos%5Ctheta%20%3D%203)
by solving above we got
![\theta = 164 degree](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20164%20degree)