Answer:
alpha=53.56rad/s
a=5784rad/s^2
Explanation:
First of all, we have to compute the time in which point D has a velocity of v=23ft/s (v0=0ft/s)
![v=v_0+at\\\\t=\frac{v}{a}=\frac{(23\frac{ft}{s})}{32.17\frac{ft}{s^2}}=0.71s](https://tex.z-dn.net/?f=v%3Dv_0%2Bat%5C%5C%5C%5Ct%3D%5Cfrac%7Bv%7D%7Ba%7D%3D%5Cfrac%7B%2823%5Cfrac%7Bft%7D%7Bs%7D%29%7D%7B32.17%5Cfrac%7Bft%7D%7Bs%5E2%7D%7D%3D0.71s)
Now, we can calculate the angular acceleration (w0=0rad/s)
![\theta=\omega_0t +\frac{1}{2}\alpha t^2\\\alpha=\frac{2\theta}{t^2}](https://tex.z-dn.net/?f=%5Ctheta%3D%5Comega_0t%20%2B%5Cfrac%7B1%7D%7B2%7D%5Calpha%20t%5E2%5C%5C%5Calpha%3D%5Cfrac%7B2%5Ctheta%7D%7Bt%5E2%7D)
![\alpha=\frac{27}{(0.71s)^2}=53.56\frac{rad}{s^2}](https://tex.z-dn.net/?f=%5Calpha%3D%5Cfrac%7B27%7D%7B%280.71s%29%5E2%7D%3D53.56%5Cfrac%7Brad%7D%7Bs%5E2%7D)
with this value we can compute the angular velocity
![\omega=\omega_0+\alpha t\\\omega = (53.56\frac{rad}{s^2})(0.71s)=38.02\frac{rad}{s}](https://tex.z-dn.net/?f=%5Comega%3D%5Comega_0%2B%5Calpha%20t%5C%5C%5Comega%20%3D%20%2853.56%5Cfrac%7Brad%7D%7Bs%5E2%7D%29%280.71s%29%3D38.02%5Cfrac%7Brad%7D%7Bs%7D)
and the tangential velocity of point B, and then the acceleration of point B:
![v_t=\omega r=(38.02\frac{rad}{s})(4)=152.11\frac{ft}{s}\\a_t=\frac{v_t^2}{r}=\frac{(152.11\frac{ft}{s})^2}{4ft}=5784\frac{rad}{s^2}](https://tex.z-dn.net/?f=v_t%3D%5Comega%20r%3D%2838.02%5Cfrac%7Brad%7D%7Bs%7D%29%284%29%3D152.11%5Cfrac%7Bft%7D%7Bs%7D%5C%5Ca_t%3D%5Cfrac%7Bv_t%5E2%7D%7Br%7D%3D%5Cfrac%7B%28152.11%5Cfrac%7Bft%7D%7Bs%7D%29%5E2%7D%7B4ft%7D%3D5784%5Cfrac%7Brad%7D%7Bs%5E2%7D)
hope this helps!!
Answer:
The formation of a rainbow is more a demonstration of the wave-like behavior of light.
Explanation:
A rainbow is caused by the interaction of sunlight with atmospheric conditions. A rainbow formation results from the refraction and reflection of light due to changes in the light's wavelength direction. Naturally, light enters a water droplet, slowing down and bending as it goes from air to denser water in a refraction as if "bent." Then light reflects off the inside of the droplet, separating into its component wavelengths or colors. With light exiting from the droplet, a rainbow is formed.
Answer:
![W = 78.48N\\W =0.0784kN\\W = 8kgf\\](https://tex.z-dn.net/?f=W%20%3D%2078.48N%5C%5CW%20%3D0.0784kN%5C%5CW%20%3D%208kgf%5C%5C)
![W= 3.6lbf\\W= 115.2 lbm*ft/s2](https://tex.z-dn.net/?f=W%3D%203.6lbf%5C%5CW%3D%20115.2%20lbm%2Aft%2Fs2)
Explanation:
if
![m=8kg=3.6lb\\](https://tex.z-dn.net/?f=m%3D8kg%3D3.6lb%5C%5C)
and g=9.81 m/s2=32.16 ft/s2
and
W=m*g
we can just replace de mass and gravity and we have
![W = 8kg * 9.81 \frac{m}{s^{2} } =78.48N\\W = \frac{78.48N}{1000} =0.0784kN\\W = 8kgf\\](https://tex.z-dn.net/?f=W%20%3D%208kg%20%2A%209.81%20%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%20%7D%20%3D78.48N%5C%5CW%20%3D%20%5Cfrac%7B78.48N%7D%7B1000%7D%20%3D0.0784kN%5C%5CW%20%3D%208kgf%5C%5C)
![W= 3.6lbf\\W= 3.6lbm *32.16 ft/s2 =115.2 lbm*ft/s2](https://tex.z-dn.net/?f=W%3D%203.6lbf%5C%5CW%3D%203.6lbm%20%2A32.16%20ft%2Fs2%20%3D115.2%20lbm%2Aft%2Fs2)
Answer:
1.995 m
Explanation:
Distance of penny as seen by the person = 5 m
Height of person from water surface = 3.50 m
Apparent depth of penny = 5 - 3.50 = 1.5 m
refractive index of water, n = 1.33
real depth / apparent depth = n
real depth = 1.33 x 1.5 = 1.995 m
Thus, the actual depth of water at that point is 1.995 m.
Moving a spring back and forth creates a longitudinal wave