Answer:
The buoyant force is 3778.8 N in upward.
Explanation:
Given that,
Mass of balloon = 222 Kg
Volume = 328 m³
Density of air = 1.20 kg/m³
Density of helium = 0.179 kg/m³
We need to calculate the buoyant force acting
Using formula of buoyant force

Where,
= density of air
V = Volume of balloon
g = acceleration due to gravity
Put the value into the formula


This buoyant force is in upward direction.
Hence, The buoyant force is 3778.8 N in upward.
Answer:
i) E = 269 [MJ] ii)v = 116 [m/s]
Explanation:
This is a problem that encompasses the work and principle of energy conservation.
In this way, we establish the equation for the principle of conservation and energy.
i)

![W_{1-2}= (F*d) - (m*g*h)\\W_{1-2}=(500000*2.5*10^3)-(40000*9.81*2.5*10^3)\\W_{1-2}= 269*10^6[J] or 269 [MJ]](https://tex.z-dn.net/?f=W_%7B1-2%7D%3D%20%28F%2Ad%29%20-%20%28m%2Ag%2Ah%29%5C%5CW_%7B1-2%7D%3D%28500000%2A2.5%2A10%5E3%29-%2840000%2A9.81%2A2.5%2A10%5E3%29%5C%5CW_%7B1-2%7D%3D%20269%2A10%5E6%5BJ%5D%20or%20269%20%5BMJ%5D)
At that point the speed 1 is equal to zero, since the maximum height achieved was 2.5 [km]. So this calculated work corresponds to the energy of the rocket.
Er = 269*10^6[J]
ii ) With the energy calculated at the previous point, we can calculate the speed developed.
![E_{k2}=0.5*m*v^2\\269*10^6=0.5*40000*v^2\\v=\sqrt{\frac{269*10^6}{0.5*40000} }\\ v=116[m/s]](https://tex.z-dn.net/?f=E_%7Bk2%7D%3D0.5%2Am%2Av%5E2%5C%5C269%2A10%5E6%3D0.5%2A40000%2Av%5E2%5C%5Cv%3D%5Csqrt%7B%5Cfrac%7B269%2A10%5E6%7D%7B0.5%2A40000%7D%20%7D%5C%5C%20v%3D116%5Bm%2Fs%5D)
Average velocity =
(displacement) / (time for the displacement)
and
(direction of the displacement) .
Displacement =
(distance from the start-point to the end-point)
and
(direction from the start-point to the end-point) .
When Ben is 200 meters from the corner store,
he is (500 - 200) = 300 meters from his house.
His displacement is
300 meters in the direction
from his house to the neighbor .
His average velocity is
(300/910) = 0.33 meters per second, in the
direction from his house to the neighbor .
If the vertical component is 29.6 m/s down, and the horizontal component
is 54.8 m/s parallel to the surface, then the magnitude of the slanty vector is
√(29.6² + 54.8²) = √(876.16 + 3003.04) = √3879.2 = 62.28 m/s .
That's 139 mph ! Wow !