Explanation:
If the distance between the bottom of the ladder and the wall is x, then:
cos θ = x / 10
Taking derivative with respect to time:
-sin θ dθ/dt = 1/10 dx/dt
Substituting for θ:
-sin (acos(x / 10)) dθ/dt = 1/10 dx/dt
Given that x = 6 and dx/dt = 1.1:
-sin (acos(6/10)) dθ/dt = 1/10 (1.1)
-0.8 dθ/dt = 0.11
dθ/dt = -0.1375
The angle is decreasing at 0.1375 rad/s.
The average speed is 615.7 mph (275.2 m/s)
Explanation:
The average speed of an object gives a measure of how fast an object is moving over a certain time interval. It is a scalar quantity, and it is calculated as follows
![v=\frac{d}{t}](https://tex.z-dn.net/?f=v%3D%5Cfrac%7Bd%7D%7Bt%7D)
where
v is the average speed
d is the distance covered
t is the time interval
For the jet in this problem, we have:
d = 1293 mi is the distance covered
t = 2.1 h is the time interval
Therefore, the average speed is:
![v=\frac{1293}{2.1}=615.7 mph](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B1293%7D%7B2.1%7D%3D615.7%20mph)
We can also convert into SI units (m/s), keeping in mind that:
![1 mi = 1609 m\\1 h = 3600 s](https://tex.z-dn.net/?f=1%20mi%20%3D%201609%20m%5C%5C1%20h%20%3D%203600%20s)
And so
![v=615.7 \frac{mi}{h}\cdot \frac{1609 m/mi}{3600 s/h}=275.2 m/s](https://tex.z-dn.net/?f=v%3D615.7%20%5Cfrac%7Bmi%7D%7Bh%7D%5Ccdot%20%5Cfrac%7B1609%20m%2Fmi%7D%7B3600%20s%2Fh%7D%3D275.2%20m%2Fs)
Learn more about average speed:
brainly.com/question/8893949
brainly.com/question/5063905
#LearnwithBrainly
Part A.
To get the acceleration of the system we consider the two blocks as a single mass. For this situation we have, from Newton's second law, that:
![T-W=(m_1+m_2)a](https://tex.z-dn.net/?f=T-W%3D%28m_1%2Bm_2%29a)
where T is the tension in the upper sting and W is the weight of the system. Solving the equation for a we have:
![\begin{gathered} 6.6-(0.3+0.24)(9.8)=(0.3+0.24)a \\ a=\frac{6.6-(0.3+0.24)(9.8)}{(0.3+0.24)} \\ a=2.42 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%206.6-%280.3%2B0.24%29%289.8%29%3D%280.3%2B0.24%29a%20%5C%5C%20a%3D%5Cfrac%7B6.6-%280.3%2B0.24%29%289.8%29%7D%7B%280.3%2B0.24%29%7D%20%5C%5C%20a%3D2.42%20%5Cend%7Bgathered%7D)
Therefore the acceleration of the system is 2.42 meters per second per second.
Part B.
Now, that we have the acceleration of the system we analyze the lower block individually; for this block the equation of motion is:
![T^{\prime}-W^{\prime}=m_2a](https://tex.z-dn.net/?f=T%5E%7B%5Cprime%7D-W%5E%7B%5Cprime%7D%3Dm_2a)
where T' is the tension in the lower rope, W' is the weight of the lower block and m2 is its mass. Solving for the tension we have that:
![\begin{gathered} T^{\prime}=(0.24)(9.8)+(0.24)(2.42) \\ T^{\prime}=2.93 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20T%5E%7B%5Cprime%7D%3D%280.24%29%289.8%29%2B%280.24%29%282.42%29%20%5C%5C%20T%5E%7B%5Cprime%7D%3D2.93%20%5Cend%7Bgathered%7D)
Therefore the tension in the lower rope is 2.93 N
Vibrating electron can emit on electromagnetic wave, the frequency of the electromagnetic wave must be equal to the vibrating frequency of electron.