0:00
All right, hello.
00:01
In this question we're told information about the pylobolus mushroom, which launches its spores out and it accelerates its spores to a speed of seven meters per second in only two microseconds, which is very fast.
00:12
We're given the mass of the spore and the height of the mushroom and we're told or asked if the spores are shot out horizontally at maximum speed, how far away from the fungi do they land, neglecting air resistance.
00:24
So i'm going to eject this at some speed, v naught here, equal to seven meters per second.
00:33
And it's going to fly, we're going to assume it has a parabolic trajectory for free fall because there's no drag, and it's going to land some distance away, x, and we want to know what that distance is.
00:46
Well, we know that our velocity in the x direction is going to be constant and we know that since we're starting all in the x direction, that's going to just be v naught and that's going to be our distance in the x direction over our time that we're traveling at this speed.
01:00
And we want to find x here.
01:02
So we know that our change in distance or x is equal to v naught times our time, but we don't know what our time is.
01:09
So in order to figure out our time, we're going to use the fact that the height of the mushroom is one centimeter.
01:15
So we know that the spore has to fall a vertical distance of one centimeter before it hits the ground.
01:21
And so we're going to use the equation, our change in height or our change in y here is going to be our initial height plus our initial speed in that direction times time plus one half times our acceleration in that direction times time squared...