The pile $\backslash ($ P $\backslash )$ shown in $($Figure $1)$ has a mass of $800$ kg and is being driven into loose sand using the $180-$kg hammer $\backslash ($ C $\backslash )$ which is dropped a distance of $0\mathrm{.}5$ m from the top of the pile. The coefficient of restitution between the hammer and the pile is $\backslash ($ e$=0\mathrm{.}1\backslash ).$ Neglect the impulses due to the weights of the pile and hammer and the impulse due to the sand during the impact.

Determine the initial speed of the pile just after it is struck by the hammer.

Express your answer to three significant figures and include the appropriate units.

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