The image for this problem can be found in the following link: http://imgur.com/

Question

The image for this problem can be found in the following link: http://imgur.com/nadQV Please show all work/formulas so that I may understand this problem for the future. Thank you very much! :) A package is pushed up an incline at x=0 with initial speed v(0). Acceleration of the package is given by a= -(gsin(theta)+nv), where g is the acceleration due to gravity, n is a constant, and v is the velocity of the package. If theta = 30 degrees, v(0) = 15 ft/s, and n=11 s^-1, find the time it takes for the package to come to a stop.

Explanation / Answer

let t be time to come to a stop a=dv/dt=-(gsin30+nv) dv/(gsin30+nv)=-dt integrating vel from 15 ft/s to 0 and time from o to t we get t=[ln(gsin30+nv)]/n from 15 to 0,n=11 g=32.2 ft/s2 t={[ln(gsin30+n*15)]-ln(gsin30)}/n=0.22 sec

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