A package is pushed up an incline at x=0 with an initial speed v(initial). The i
ID: 1860376 • Letter: A
Question
A package is pushed up an incline at x=0 with an initial speed v(initial). The incline is coated with a thin viscous layer so that the acceleration of the package is given by a=-g(sin(theta)+nv), where g is the acceleration due to gravity, n is a constant, and v is the velocity of the package. If theta=30degrees, v(initial=16ft/s, and n=7s^-1, determine the time is takes for the package to come to a stop. Please show steps of your work. Picture is hard to see, but x is the distance from the bottom of the incline to the back of the package, theta is the angle between incline and ground, and v is the arrow pointing above package uphill.
A package is pushed up an incline at x=0 with an initial speed v(initial). The incline is coated with a thin viscous layer so that the acceleration of the package is given by a=-g(sin(theta)+nv), where g is the acceleration due to gravity, n is a constant, and v is the velocity of the package. If theta=30degrees, v(initial=16ft/s, and n=7s^-1, determine the time is takes for the package to come to a stop. Please show steps of your work. Picture is hard to see, but x is the distance from the bottom of the incline to the back of the package, theta is the angle between incline and ground, and v is the arrow pointing above package uphill.Explanation / Answer
a = -(gsin(30) + (1/7)(16)) = -((g/2) + (16/7))
Vo = 16
Vf = 0
Vf = Vo + at
0 = Vo + at
-Vo / a = t
-16 / [-((g/2) + (16/7))]
-16 / [-(16 + (16/7))]
-16 / [-128/7]
t = approx 0.875 seconds
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