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valentinak56 [21]
3 years ago
7

A cubical water tank with edges measuring 10 feet in length is initially full of water. If the tank were then to lose water at a

constant rate of 10 cubic feet per second, in how many seconds would the tank be full?
Physics
1 answer:
pentagon [3]3 years ago
7 0

Answer:

100 secs

Explanation:

edge of the cubical tank = 10 feet

volume of the cube is = edge^3

therefore volume = 10^3= 1000 cubic feet

discharge from the pipe Q= 10 cubic feet per second

time taken to fill the tank t= V/Q = 1000/10= 100 secs

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Explanation:

Let

x_1 = distance traveled while accelerating

x_2 = distance traveled while decelerating

The distance traveled while accelerating is given by

x_1 = v_0t + \frac{1}{2}at^2 = \frac{1}{2}at^2

\:\:\:\:\:= \frac{1}{2}(2.5\:\text{m/s}^2)(30\:\text{s})^2

\:\:\:\:\:= 1125\:\text{m}

We need the velocity of the rocket after 30 seconds and we can calculate it as follows:

v = at = (2.5\:\text{m/s}^2)(30\:\text{s}) = 75\:\text{m/s}

This will be the initial velocity when start calculating for the distance it traveled while decelerating.

v^2 = v_0^2 + 2ax_2

0 = (75\:\text{m/s})^2 + 2(-0.65\:\text{m/s}^2)x_2

Solving for x_2, we get

x_2 = \dfrac{(75\:\text{m/s})^2}{2(0.65\:\text{m/s}^2)}

\:\:\:\:\:= 4327\:\text{m}

Therefore, the total distance x is

x = x_1 + x_2 = 1125\:\text{m} + 4327\:\text{m}

\:\:\:\:= 5452\:\text{m}

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