a mountain climber looks up and sees an avalanche of boulders accelerating towards her. The boulders are initially 60m above, moving at 4.00m/s^2. The climber reacts in 0.500s and begins to run down the slope. At what speed must she run in order to reach the bottom of the slope, 30.0m below, before the boulders?

Question

anonymous · Answer

First, she should probably turn and run perpendicular to the slide. Probably not the answer you're looking for, though. :)

Start by finding the distance traveled by the boulders in the time it takes her to react. The time the boulders travel and the time the girl travels will be the same, so you'll need to have two equations solved for t. One for the girl, one for the boulders. Set them equal to each other and that will give you the speed for the tie.

anonymous · Answer

@eighthourlunch , I was going to ask if i should use the equation of motion for vertical or horizontal motion

anonymous · Answer

Technically, the equations for displacement under uniform acceleration are going to be the same in any direction--up, down, diagonally, etc. You have the acceleration of the boulder so you can use that to find the first .500 seconds as though it were flat. The way that the question is phrased makes it look like the runner's velocity is constant, so for the runner: $$s=vt$$For the boulder:$$s=v_0t+1/2at^2$$.

anonymous · Answer

Maybe this drawing will help. Sorry, I don't have my sketchbook handy, or it'd be a little more clear.