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A box with an initial speed of #5 m/s# is moving up a ramp. The ramp has a kinetic friction coefficient of #3/7 # and an incline of #(3 pi )/8 #. How far along the ramp will the box go?

Answer 1

Olivia Askew

The distance is #=1.17m#

Solving in the direction of the plane #↗^+#

#mu_k=F_k/N#

#F_k=mu_kN#

#N=mgcostheta#

#F_k=mu_kmgcostheta#

The component of the weight is

#=mgsintheta#

Applying Newton' second Law

#-mu_kmgcostheta-mgsintheta=ma#

Therefore,

#a=-u_kgcostheta-gsintheta#

#=-3/7*g*cos(3/8pi)-g*sin(3/8pi)#

#=-10.66ms^-2#

The initial velocity is #u=5ms^-1#

We apply the equation of motion

#v^2=u^2+2as#

#0=5^2-2*10.66s#

#s=25/(2*10.66)#

#=1.17m#

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Answer 2

Adrian Ayala

To find the distance along the ramp the box will go, we need to use the equations of motion and apply the principles of physics, including friction and the angle of the incline. First, calculate the acceleration of the box along the incline using Newton's second law. Then, apply the equations of motion to determine the distance traveled.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.