Who would get to the bottom of the mountain faster?

Question

If two snowboarders on top of a mountain let gravity pull them to the bottom of the slope, who would reach the bottom first if snowboarder #1 weighs 70 pounds more than snowboarder #2 and there was no wind or ground resistance?

Additional info (if needed): Slope of the mountain has a 30 degree decline.

Answer 1

They would arrive at the same time. This is a similar question to dropping two things of different weight from a tower. Gravity acts on both equally.

Answer 2

Weight has no bearing on the rate of acceleration under the force of gravity alone. This follows because g = GM/R^2; so at a fixed distance R from Earth's center of mass M, g is a fixed value since G is a constant. Thus W = Mg > mg = w; where the weights are proportional to the masses M and m, and W/M = g = w/m.

This relationship simply states that when something weighs more than something else at a given distance R from Earth's mass center, that thing's mass will be proportionately bigger as well. And that keeps g, the acceleration due to gravity alone, at a constant value.

As the two snowboarders will be accelerating at the same rate (g), when all else is the same, including the drop line, their time to the bottom, starting with the same velocity and from the same height, will be the same. This follows from S = 1/2 gt^2; so that since S, the distance traveled, is the same for both and g is the same no matter what they weigh, we have 2S/g = t^2 = 2S/g.

Answer 3

Without any resistive forces (wind or friction), both will accelerate constantly, and both will reach the bottom simultaneously. If there were any resistance, the one with more mass would get to the bottom first.

Answer 4

If ignoring everything, then they will reach it at the same time because the pull of earths gravity near the earths surface is 9.81 m/s^2 always. (This is assuming the same starting velocity as well). I hope that's right.