Answer:
(A) 88.92 cm
(B) 22.22 cm
Explanation:
distance (s) = 200 cm = 0.2 m
initial velocity (v) = 0 m/s
acceleration due to gravity (g) = 9.8 m/s^{2}
lets first find the time (T) it takes for the first drop to strike the floor
from s = ut + 
200 = 0 + 
200 = 
200 / 4.9 = 
T = 6.4
(A) When the first drop strikes the floor, how far below the nozzle is the second drop.
we can find how far the second drop was when the first drop hits the ground from the formula s = ut + 
where
- s = distance
- u = initial velocity = 0
- t = time, since the drops fall at regular (equal) intervals of time, the first drop striking the floor at the instant the fourth drop begins to fall there wold be 3 time intervals and this can be seen illustrated in the attached diagram. therefore the time of the second drop = 2/3 of the time it takes the first drop to strike the ground (
) - a = acceleration due to gravity = 9.8 m/s^{2}
substituting all required values we have
s = 0 + (
)
s = 0 + (
)
s = 88.92 cm
(B) When the first drop strikes the floor, how far below the nozzle is the third drop.
we can find how far the third drop was when the first drop hits the ground from the formula s = ut + 
where
- s = distance
- u = initial velocity = 0
- t = time, since the drops fall at regular (equal) intervals of time, the first drop striking the floor at the instant the fourth drop begins to fall there wold be 3 time intervals and this can be seen illustrated in the attached diagram. therefore the time of the third drop = 1/3 of the time it takes the first drop to strike the ground (
) - a = acceleration due to gravity = 9.8 m/s^{2}
substituting all required values we have
s = 0 + (
)
s = 0 + (
)
s = 22.22 cm
During the period of 2 hours, the yeast ate the sugar, and generated Carbon-Dioxide gas and alcohol. This is the process that causes bread-dough to rise, and eventually produces stuff that can be distilled to concentrate the alcohol and make wine or whiskey.
-- If Daniel tied the neck of the balloon, so that nothing could get in r out during the 2 hours, then the mass of the balloon and everything inside it didn't change. The balloon may have inflated slightly ... due to the creation of gas inside that wasn't there before ... just like bread dough. But no mass was created or destroyed inside or outside of the balloon, and none got in or out.
-- If Daniel left the neck of the balloon open, then the mass of the balloon and its contents decreased slightly during the 2 hours. The yeast took carbon and oxygen from the sugar, and used them to make Carbon Dioxide gas. Then the gas flew out through the neck of the balloon to Freedom.