A skier begins skiing straight down a hill having a constant slope, starting from rest. If friction is negligible, as the skier goes down the hill, his/her acceleration

Question

BlackTom AI · Accepted Answer

To analyze the motion, imagine the skier on a frictionless track with a fixed incline angle. The component of gravity along the slope provides the acceleration, which is a = g sin(theta).
Option 1: 'is constant, with a value less than 9.8 m/s^2' This is correct because on a fixed incline with negligible friction, the acceleration along the slope is constant and equal to g sin(theta), which is always less than g = 9.8 m/s^2 for any angle theta between 0 and 90 degrees.
Option 2: 'is constant, with a value of roughly 9.8 m/s^2' This would imply theta is 90 degrees (a vertical drop), giving a = g, but an incline less than vertical yields a smaller value; thus this option is generally incorrect.
Option 3: 'increases with time.' On a frictionless plane with a constant slope, there is no changing force component along the slope, so the acceleration does not increase; it remains constant, making this statement false.
Option 4: 'is zero.' Starting from rest and sliding down a slope under gravity with no friction means there is a net force along the slope, so the acceleration cannot be zero; this is incorrect.

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A skier begins skiing straight down a hill having a constant slope, starting from rest. If friction is negligible, as the skier goes down the hill, his/her acceleration

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