The answer to this question is a) sulfur
Answer:
The tension is ![T = 4326.7 \ N](https://tex.z-dn.net/?f=T%20%20%3D%204326.7%20%5C%20%20N)
Explanation:
From the question we are told that
The total mass is ![m = 200 \ kg](https://tex.z-dn.net/?f=m%20%20%3D%20%20200%20%5C%20%20kg)
The radius is ![r = 5 \ m](https://tex.z-dn.net/?f=r%20%3D%205%20%5C%20%20m)
The density of air is ![\rho_a = 1.225 \ kg/m^3](https://tex.z-dn.net/?f=%5Crho_a%20%20%3D%20%201.225%20%5C%20kg%2Fm%5E3)
Generally the upward force acting on the balloon is mathematically represented as
![F_N = T + mg](https://tex.z-dn.net/?f=F_N%20%20%3D%20%20%20T%20%20%2B%20mg)
=> ![(\rho_a * V * g ) = T + mg](https://tex.z-dn.net/?f=%28%5Crho_a%20%20%2A%20%20V%20%20%2A%20%20g%20%29%20%3D%20%20%20T%20%20%2B%20mg)
=> ![T = (\rho_a * V * g ) - mg](https://tex.z-dn.net/?f=T%20%20%3D%20%20%28%5Crho_a%20%20%2A%20V%20%20%2A%20%20g%20%20%20%29%20%20-%20mg)
Here V is the volume of the spherical helium filled balloon which is mathematically represented as
![V = \frac{4}{3} * \pi r^3](https://tex.z-dn.net/?f=V%20%20%3D%20%20%5Cfrac%7B4%7D%7B3%7D%20%20%2A%20%5Cpi%20r%5E3)
=> ![V = \frac{4}{3} * 3.142 *(5)^3](https://tex.z-dn.net/?f=V%20%20%3D%20%20%5Cfrac%7B4%7D%7B3%7D%20%20%2A%203.142%20%2A%285%29%5E3)
=> ![V = 523.67\ m^3](https://tex.z-dn.net/?f=V%20%20%3D%20523.67%5C%20%20m%5E3)
So
![T = (1.225 * 523.67* 9.8 ) - 200 * 9.8](https://tex.z-dn.net/?f=T%20%20%3D%20%281.225%20%2A%20%20523.67%2A%20%209.8%20%29%20-%20%20200%20%2A%20%209.8)
![T = 4326.7 \ N](https://tex.z-dn.net/?f=T%20%20%3D%204326.7%20%5C%20%20N)
Answer:
Explanation:
Given
For first case
launch angle ![\theta =45^{\circ}C](https://tex.z-dn.net/?f=%5Ctheta%20%3D45%5E%7B%5Ccirc%7DC)
at highest point ![h=150 m/s](https://tex.z-dn.net/?f=h%3D150%20m%2Fs)
![150=u\cos 45](https://tex.z-dn.net/?f=150%3Du%5Ccos%2045)
![u=\frac{150}{\cos 45}=212.132 m/s](https://tex.z-dn.net/?f=u%3D%5Cfrac%7B150%7D%7B%5Ccos%2045%7D%3D212.132%20m%2Fs)
For second case
![\theta _2=37^{\circ}C](https://tex.z-dn.net/?f=%5Ctheta%20_2%3D37%5E%7B%5Ccirc%7DC)
at highest Point velocity is ![u\cos \theta _2](https://tex.z-dn.net/?f=u%5Ccos%20%5Ctheta%20_2)
![=212.132\times \cos 37](https://tex.z-dn.net/?f=%3D212.132%5Ctimes%20%5Ccos%2037)
as there is no acceleration in x direction therefore horizontal velocity is same