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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BlackTom AI · Accepted Answer

Consider the scenario: a skier on a frictionless hill with a constant slope, starting from rest. The acceleration along the slope results from gravity with a component g sin(theta) along the incline, where theta is the incline angle. This acceleration is constant in magnitude because theta is constant and there are no non-conservative forces (friction) altering it.

Option 1: "is constant, with a value of roughly 9.8 m/s2". This would imply the acceleration equals g, which would occur only if the incline were vertical (theta = 90°). In a typical downhill incline, theta < 90°, so the component of gravity along the slope is less than g. Therefore, this statement is incorrect.

Option 2: "increases with time." Since acceleration along the slope is g sin(theta) and theta is constant, there is no time-dependent change in acceleration. The velocity changes due to constant acceleration, but the acceleration itself stays the same. Hence this option is incorrect.

Option 3: "is constant, with a value less than 9.8 m/s2". This aligns with the physics: the downhill acceleration is a constant g sin(theta), which is greater than zero for any non-vertical slope and less than g for any slope with theta < 90°. Therefore, the magnitude is constant and less than 9.8 m/s2 for a typical incline, making this statement correct.

Option 4: "is zero." A zero acceleration would imply no motion change in velocity, contradicting the starting from rest and the presence of gravity along the slope. Since gravity has a component along the incline, acceleration cannot be zero. This option is incorrect.

SPHY001 Practice Quiz - Unit 05 | LA045

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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