Answer:
![y = 17.04 ft](https://tex.z-dn.net/?f=y%20%3D%2017.04%20ft)
Explanation:
Since the cable touches the road at the mid point of two towers
so here we have vertex at that mid point taken to be origin
now the maximum height on the either side is given as
![y = 180 ft](https://tex.z-dn.net/?f=y%20%3D%20180%20ft)
horizontal distance of the tower from mid point is given as
![x = \frac{1300}{2} = 650 ft](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B1300%7D%7B2%7D%20%3D%20650%20ft)
now from the equation of parabola we have
![y = k x^2](https://tex.z-dn.net/?f=y%20%3D%20k%20x%5E2)
![180 = k(650^2)](https://tex.z-dn.net/?f=180%20%3D%20k%28650%5E2%29)
![k = 4.26 \times 10^{-4}](https://tex.z-dn.net/?f=k%20%3D%204.26%20%5Ctimes%2010%5E%7B-4%7D)
now we have
![y = (4.26 \times 10^{-4})x^2](https://tex.z-dn.net/?f=y%20%3D%20%284.26%20%5Ctimes%2010%5E%7B-4%7D%29x%5E2)
now we need to find the height at distance of 200 ft from center
so we have
![y = (4.26 \times 10^{-4})(200^2)](https://tex.z-dn.net/?f=y%20%3D%20%284.26%20%5Ctimes%2010%5E%7B-4%7D%29%28200%5E2%29)
![y = 17.04 ft](https://tex.z-dn.net/?f=y%20%3D%2017.04%20ft)
Answer:
The horizontal velocity is ![v = 9.2 m/s](https://tex.z-dn.net/?f=v%20%3D%209.2%20m%2Fs)
Explanation:
From the question we are told that
The mass of the pumpkin is ![m = 2.8 \ kg](https://tex.z-dn.net/?f=m%20%3D%202.8%20%5C%20kg)
The distance of the the car from the building's base is ![d = 13.4 \ m](https://tex.z-dn.net/?f=d%20%3D%2013.4%20%5C%20m)
The height of the roof is ![h = 10.4 \ m](https://tex.z-dn.net/?f=h%20%3D%2010.4%20%5C%20m)
The height is mathematically represented as
![h = \frac{1}{2} gt^2](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20gt%5E2)
Where g is the acceleration due to gravity which has a value of ![g =9.8 \ m/s^2](https://tex.z-dn.net/?f=g%20%3D9.8%20%5C%20m%2Fs%5E2)
substituting values
![10.4= 0.5 * 9.8 * t](https://tex.z-dn.net/?f=10.4%3D%200.5%20%2A%209.8%20%2A%20t)
making the time taken the subject of the formula
![t = \frac{10.4}{0.5 * 9.8 }](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B10.4%7D%7B0.5%20%2A%209.8%20%7D)
![t = 1.457 \ s](https://tex.z-dn.net/?f=t%20%3D%201.457%20%5C%20s)
The speed at which the pumpkin move horizontally can be represented mathematically as
![v = \frac{d}{t}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7Bd%7D%7Bt%7D)
substituting values
![v =\frac{13.4}{1.457}](https://tex.z-dn.net/?f=v%20%3D%5Cfrac%7B13.4%7D%7B1.457%7D)
![v = 9.2 m/s](https://tex.z-dn.net/?f=v%20%3D%209.2%20m%2Fs)
The correct answer is: Option (A) 75 J
Explanation:
First, be careful with the units here. As you can see it is mentioned that there is a 50N box. It means that the weight (<em>mg</em>) of the box is given as the unit is <em>Newton</em>, not its mass (which is in kg).
As,
Potential-energy = mass * acceleration-due-to-gravity * height
PE = m*g*h --- (A)
In equation (A), mg is actually the weight of the box, which is given.
mg = 50N
h = height = 1.5m
Plug the values in equation (A):
PE = 50 * 1.5 = <em>75 J (Option A)</em>
Angstrom = 10^-10 m
for nucleus size are used fermi (femtometer 10^-15 m )