Two stones are thrown simultaneously one straight upward...

Two stones are thrown simultaneously, one straight upward from the base of a cliff and the other straight downward from the top of the cliff. The height of the cliff is 6.12 m. The stones are thrown with the same speed of 8.20 m/s. Find the location (above the base of the cliff) of the point where the stones cross paths.

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Transcript

00:01 Okay, we have two stones being thrown.

00:05 One is thrown upward from the base of a cliff.

00:11 So let's do the stones in red.

00:16 So one's thrown upward with speed v, and one's thrown downward with speed v.

00:24 We're given the height of this cliff.

00:26 We'll call it h.

00:28 6 .12 meters.

00:30 They both have the same speed v.

00:32 V is 8 .2 meters per second.

00:38 What location above the base of the cliff will the stones cross paths? so let's just guess, we'll put it right there, that x, and we're gonna call that position y final.

00:53 We're gonna measure y from the base of the cliff upward.

00:58 So we have two things going on here.

01:03 Let's call these rocks rock a and rock b.

01:09 So let's write down the motion equations for these two.

01:12 So for rock a, we get y final.

01:16 The place they meet is equal to the initial position h plus the initial velocity times time.

01:24 The initial velocity is down.

01:26 And then minus 1 .5 gt squared since we're in freefall.

01:30 For rock b, we have y final equals y initial, which is zero.

01:37 Plus the initial velocity times time minus one half g t squared.

01:45 Well, they are going to have the same y final at the same time, right? so those are all going to be equal...