In an assembly$-$line process, the $20-$kg$$package AA starts from $3$ m$/$s$$ at the position shown, and slides down the smooth$$ramp$.$ Suppose that you want to design the hydraulic$$device BB to exert a force of magnitude F$=540(1+0\mathrm{.}4$t$)$F$=540(1+0\mathrm{.}4$t$)$ N on the package, where tt is in seconds measured from the time of the first contact. You are required to find:

$-$ the velocity of the package at the time of first contact with the hydraulic device

$-$ the time required to bring the package to rest

Then choose two correct answers from the following:

Question $6$Answer

The package will come to stop in $0\mathrm{.}23$ s after the first contact with the device.

The average force exerted by the hydraulic device$$ is equal to $465\mathrm{.}2$ N$.$

The normal reaction on the package exerted by the surface and the weight component perpendicular to the surface have no impulse.$$

From the starting point to the point at which the package come to first contact with the device, the package travels with the acceleration of $9\mathrm{.}81$ m$/$s$22.$

The package will come to stop in $0\mathrm{.}71$ s after the first contact with the device.

The velocity of the package at the time of first contact with the hydraulic device $9+23$g$9+23$g m$/$s$,$ where g$=9\mathrm{.}81$g$=9\mathrm{.}81$m$/$s$22.$ In an assembly$-$line process, the $20-$kg package $\backslash ($ A $\backslash )$ starts from $\backslash (3\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ at the position shown, and slides down the smooth ramp. Suppose that you want to design the hydraulic device $\backslash ($ B $\backslash )$ to exert a force of magnitude $\backslash ($ F$=540(1+0\mathrm{.}4$ t$)\backslash$mathrm$\{$N$\}\backslash )$ on the package, where $\backslash ($ t $\backslash )$ is in seconds measured from the time of the first contact. You are required to find:

$-$ the velocity of the package at the time of first contact with the hydraulic device

$-$ the time required to bring the package to rest

Then choose two correct answers from the following:The package will come to stop in $0\mathrm{.}23$ s after the first contact with the device.The average force exerted by the hydraulic device is equal to $465\mathrm{.}2$ N $.$The normal reaction on the package exerted by the surface and the weight component perpendicular to the surface have no impulse.From the starting point to the point at which the package come to first contact with the device, the package travels with the acceleration of $\backslash (9\mathrm{.}81\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}^\{2\}\backslash ).$The package will come to stop in $0\mathrm{.}71$ s after the first contact with the device.The velocity of the package at the time of first contact with the hydraulic device $\backslash (\backslash$sqrt$\{9+2\backslash$sqrt$\{3\}$ g$\}\backslash )\backslash (\backslash$mathrm$\{$m$\}/\backslash$mathrm$\{$s$\}\backslash ),$ where $\backslash ($ g$=9\mathrm{.}81\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}^\{2\}\backslash ).$