We'll use kinematics equations and Bernoulli's continuity equation to solve this problem.

Uniformly accelerated motion (UAM) equations:

$\overline{)\mathbf{}{{\mathit{v}}}_{{\mathit{f}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{\mathit{v}}}_{{\mathbf{0}}}{\mathbf{}}{\mathbf{-}}{\mathit{g}}{\mathit{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathit{y}}{\mathbf{=}}{\mathbf{}}\mathbf{\left(}\frac{{\mathit{v}}_{\mathit{f}}\mathbf{+}{\mathit{v}}_{\mathbf{0}}}{\mathbf{2}}\mathbf{\right)}{\mathit{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathit{y}}{\mathbf{=}}{\mathbf{}}{{\mathit{v}}}_{{\mathbf{0}}}{\mathit{t}}{\mathbf{-}}\frac{\mathbf{1}}{\mathbf{2}}{\mathit{g}}{{\mathit{t}}}^{{\mathbf{2}}}\phantom{\rule{0ex}{0ex}}{\mathbf{}}{{{\mathit{v}}}_{{\mathit{f}}}}^{{\mathbf{2}}}{\mathbf{=}}{\mathbf{}}{{{\mathit{v}}}_{{\mathbf{0}}}}^{{\mathbf{2}}}{\mathbf{}}{\mathbf{-}}{\mathbf{2}}{\mathit{g}}{\mathbf{\u2206}}{\mathit{y}}}$

Bernoulli's continuity equation:

$\overline{){\mathbf{Av}}{\mathbf{=}}{\mathit{c}}{\mathit{o}}{\mathit{n}}{\mathit{s}}{\mathbf{tan}}{\mathit{t}}}$

**(a)**

We'll use the continuity equation to solve for the velocity

Flow rate = Av

v = Flow rate/v

A nozzle with a radius of .33 cm is attached to a garden hose with a radius of .85 cm. the flow rate through hose and nozzle is .55 L/s.

a. Calculate the maximum height to which water could be squirted with the hose if it emerges from the nozzle in m.

b. Calculate the maximum height (in cm) to which water could be squirted with the hose if it emerges with the nozzle removed, assuming the same flow rate.

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