A package delivery service (we cannot say any names but their initials are F and E), has asked your help in designing a system to bring packages that have been sliding along delivery chutes before they get loaded onto the trucks. The packages, with a mass of 5 kilogram, are stationary at the top and then they slide down a chute that is 5 meter high. The delivery chute has rollers along it which make it virtually frictionless. The delivery chute makes and angle of 25.9o. A stopping spring is located at the very end of the entire chute but the -3.8 meter wide horizontal slowing chute between the bottom of the delivery chute and right in front of the spring does not have rollers and is not frictionless (uk=0.21). The stopping spring has a spring constant of 490 N/m. For simplicity, suppose the chute under the spring is frictionless, otherwise the math gets ugly.

Find the speed of package at the bottom of the chute?

in m/s

Find the speed of the box just before hitting the stopping spring?

in m/s

Find how far is the stopping spring compressed as it brings the package to a stop?

in m