A $127$ kg box needs to be lifted to put on the back of a ute. The box is too heavy to be lifted directly onto the tray, $1\mathrm{.}1$ m high. You decide to use a frictionless ramp to slide the box from the ground onto the tray.

$($a$)$ Draw a diagram, listing all relevant information

$($b$)$ Calculate the work required to lift the box onto the tray

$($c$)$ If you wish to only use $40\%$ of the force on the ramp, compared to lifting directly vertical, what length and angle should the ramp be$?$