<span>Answer:
I'm pretty sure the SA / V ratio would get smaller. Assume that the cell is more or less spherical. SA = 4(pi)r^2, while V = (3/4)(pi)r^3. The ratio = (4(pi)r^2)/((3/4)(pi)r^3), which can be simplified to 3/r. Thus, the larger r gets, the smaller the ratio becomes.</span>
r(t) models the water flow rate, so the total amount of water that has flowed out of the tank can be calculated by integrating r(t) with respect to time t on the interval t = [0, 35]min
∫r(t)dt, t = [0, 35]
= ∫(300-6t)dt, t = [0, 35]
= 300t-3t², t = [0, 35]
= 300(35) - 3(35)² - 300(0) + 3(0)²
= 6825 liters
The distance you free-fall from rest is D = (1/2) (g) (T²) <== memorize this
Height of the platform = (1/2) (9.8 m/s²) (2.4 sec)²
Height = (4.9 m/s²) (5.76 s²)
Height = (4.9/5.76) meters
Height = 28.2 meters (a VERY high platform ... about 93 ft off the water !)
Without air-resistance, your horizontal speed doesn't change. It's constant. Traveling 3.1 m/s for 2.4 sec, you cover (3.1 m/s x 2/4 s) = 7.4 m horizontally.
