A $150$ lb crate is released from rest along a $25$ inclined plane. The coefficient of kinetic friction between the crate and the plane is $k=0\mathrm{.}3.$ The crate slides $30$ ft down the plane. What is the final velocity of the crate? Solve this problem using three different methods.

The equations of motion

The principle of work and energy

The principle of linear impulse and momentum

Note: You should get same answer using the different methods. Show your work and the equations used. Draw a complete FBD for the problem.