A $60-$lb box slides from rest down the smooth ramp onto the surface of a $20-$lb cart shown in $($Figure $1).$ Assume $\backslash ($ h$=15\backslash$mathrm$\{$ft$\}\backslash ).$

Part A

Determine the speed of the box at the instant it stops sliding on the cart.

Express your answer in feet per second to three significant figures.

Part B

If someone ties the cart to the ramp at $\backslash ($ B $\backslash ),$ determine the horizontal impulse the box will exert at $\backslash ($ C $\backslash )$ in order to stop its motion. Neglect friction and the size of the box.

Express your answer in pound$-$seconds to three significant figures.

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I$=$

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$\backslash (\backslash$mathrm$\{$lb$\}\backslash$cdot $\backslash$mathrm$\{$s$\}\backslash )$