Question

A cylinder that is 20 cm tall is filled with water. If a hole is made in the side of the cylinder 5 cm below the top level, how far will the stream land from the base of the cylinder? Assume that the cylinder is large enough so that the level of the water in the cylinder does not drop significantly.

Answer 1

Answer:

See description

Explanation:

This is an example where we need Tornicelli's law, which states that the horizontal speed of a fluid that starts falling from an orifice is the same speed that an object acquires from free-falling.

$v = \sqrt{2gh}$

we are given:

$h_{cilinder} = 0.2 [m]\\h = 0.05 [m]\\d=0.15[m]$

the horizontal velocity of the water at the start is:

$v = \sqrt{2(9.8)(0.05)}=0.989949 [m/s]=1[m/s]$

now we need to find the time for the water drops to fall d:

as the gravity is the only force interacting with the water we have:

$y(t) = \frac{1}{2} g*t^2$

replace for y = d

$0.15 = \frac{1}{2} g*t^2=>t=\sqrt{\frac{2*0.15}{9.8}}=0.1749[s]$

now that we have t we notice that there are no horizontal forces interacting with the water, so the horizontal position is given by:

$x(t)=v*t$

Finally, we replace v and t:

$x(2.45) = 1*0.1749 = 0.1749 [m]=17.49[cm]$