$6$

In an assembly$-$line process, the $20-$kg package A starts from $3\frac{m}{s}$ at the position shown, and slides down the smooth ramp. Suppose that you want to design the hydraulic device $B$ to exert a force of magnitude $F=540(1+0\mathrm{.}4t)N$ on the package, where $t$ 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 average force exerted by the hydraulic device is equal to $465\mathrm{.}2$ N $.$

The velocity of the package at the time of first contact with the hydraulic device $\sqrt[\phantom{2}]{9+2\sqrt[\phantom{2}]{3}g}\frac{m}{s},$ where $g=9\mathrm{.}81\frac{m}{s^2}.$

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

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 $9\mathrm{.}81\frac{m}{s^2}.$

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

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