 #1
mcastillo356
Gold Member
 279
 146
 Homework Statement:

A skier goes down a slope of 58% (30º). Ignoring friction, calculate:
a) The ##x## and ##y## components of the acceleration (parallel and perpendicular to the slope)
b) If it starts from repose, calculate the velocity it will have within one minute
c) Draw a diagram with all the vectors that play part in the exercise, and name them properly
 Relevant Equations:

Newton's second law
Basic kinematics
a) ##a_y=\dfrac{\sum{F_y}}{m}=\dfrac{Nmg\cos{\alpha}}{m}=(1\cos{\alpha})g##
##a_x=\dfrac{\sum{F_x}}{m}=\dfrac{mg\sin{\alpha}}{m}=g\sin{\alpha}##
##a_y=(10,866)9,81\;m/s^2=1,31\;m/s^2##
##a_x=(0,5)9,81\;m/s^2=4,91\;m/s^2##
How can it be a perpendicular acceleration?; which coordinate system am I using?. I've solved it without no clue, just Newton's 2nd law.
b)##v_x=a_x\cdot{t}=4,91\;m/s^2\cdot{60\;s}=295\;m/s##
##v_y=a_y\cdot{t}=1,31\;m/s^2\cdot{60\;s}=78,6\;m/s##
##v=\sqrt{8,70\cdot{10^4\;m^2/s^2}+0,618\cdot{10^4\;m^2/s^2}}=305\;m/s##
Does it make sense?
c) I've found a picture (the first shown in the link's article), but I think there are too many vectors. The only vectors that play part, from my point of view, are ##\vec{N}## and weight
https://www.wikiwand.com/es/Plano_inclinado
##a_x=\dfrac{\sum{F_x}}{m}=\dfrac{mg\sin{\alpha}}{m}=g\sin{\alpha}##
##a_y=(10,866)9,81\;m/s^2=1,31\;m/s^2##
##a_x=(0,5)9,81\;m/s^2=4,91\;m/s^2##
How can it be a perpendicular acceleration?; which coordinate system am I using?. I've solved it without no clue, just Newton's 2nd law.
b)##v_x=a_x\cdot{t}=4,91\;m/s^2\cdot{60\;s}=295\;m/s##
##v_y=a_y\cdot{t}=1,31\;m/s^2\cdot{60\;s}=78,6\;m/s##
##v=\sqrt{8,70\cdot{10^4\;m^2/s^2}+0,618\cdot{10^4\;m^2/s^2}}=305\;m/s##
Does it make sense?
c) I've found a picture (the first shown in the link's article), but I think there are too many vectors. The only vectors that play part, from my point of view, are ##\vec{N}## and weight
https://www.wikiwand.com/es/Plano_inclinado