My answer doesn't make sense. I will show question then my work: A city holding tank for water sits 20 m above the city. If a house was on fire 15 m
away from the base of the holding tank, and the tank was originally filled to a depth of
15 m, to what depth would firefighters have to drain the tank so water, sprayed from
the bottom of the tank, hits the bottom of the house?
step1: Viy=0, a=g=9.8m/s/s, dy=20
dy=Viyt + 1/2 at^2 -->
t = sqrt(40m/9.8m/s/s)= 2.02s
Step2: Vx=dx/t and Vx=15m/2.02s=7.43m/s
Step 3: change in x = 15m (distance house from water tower) and change in h (depth of water) = 15m
change in X = Vx(sqrt(2h/g) or
h = [(x^2)(g)]/[(Vx^2)(2)]
h = ((15^2)(9.8)]/[(7.43^2)(2)] m
h= 19.97m
That's more meters than I have. Not sure what I missed.
To determine the depth to which firefighters would have to drain the tank so that water sprayed from the bottom hits the bottom of the house, you are on the right track with the following steps:
Step 1: Calculate the time it takes for the water to fall from the holding tank to the ground. You correctly used the equation dy = Viyt + 1/2at^2, where dy is the vertical displacement, Viy is the initial vertical velocity, a is acceleration (which is the acceleration due to gravity, g), and t is time. Plugging in the values, you correctly found t = sqrt(40m/9.8m/s²) ≈ 2.02s.
Step 2: Calculate the horizontal velocity, Vx, using the formula Vx = dx/t, where dx is the horizontal displacement and t is the time calculated in Step 1. You correctly found Vx = 15m/2.02s ≈ 7.43m/s.
However, the error occurs in Step 3. The equation you used to determine the height, h, is incorrect. The correct equation is dy = Vy*t + 1/2*a*t². In this case, Vy is the vertical component of the velocity and a is acceleration. Since the only vertical component of the velocity is due to gravity, Vy = g*t.
Using dy = Vy*t + 1/2*a*t², we can substitute Vy = g*t and a = g, resulting in dy = g*t²/2. We know dy = 15m (distance house from water tank), so we can calculate h as follows:
15m = (9.8m/s²)*(2.02s)²/2
15m = 19.8m
To determine the depth of the water needed to hit the bottom of the house, we subtract the height of the tank from the calculated h:
h = 19.8m - 20m = -0.2m
This means that the water needs to be drained from the tank to a depth of 0.2 meters (or 20 centimeters) in order to hit the bottom of the house.