A bartender wants to put a bottle back on the top shelf but...

a bartender wants to put a bottle back on the top shelf but instead of using a step stool she wants to throw it. to make sure the bottle doesnt break she wants the bottle to reach the shelf with no y velocity. her current distance to the edge of the shelf is x=2 and y=1

Transcript

00:01 Okay, so we're given that the vertical height is 9 meters, horizontal is 9 .5.

00:06 We know the acceleration in the y is negative 9 .8, and the x is 0.

00:10 And then the final velocity in the y should be 0 because it reaches the maximum height when it reaches the window.

00:16 Okay, we want to find the initial velocity in the y and the time, and we can eventually find the final velocity in the x, initial velocity in the x, et cetera.

00:27 So let's start with the left side here and use the equation vf squared.

00:31 Is equal to v i squared plus two a delta y.

00:37 Okay, and so vf is going to be zero.

00:39 V i is going to be our unknown.

00:43 A is negative 9 .8, and delta y is 9.

00:49 Okay, so negative v .i squared is going to be equal to negative 176 .4.

01:01 So dividing by negative 1 and square rooting gives us 13 .28 meters per second, and this is our v -i -y.

01:16 So 13 .28.

01:22 Okay, we also want another time.

01:25 So if i calculate the time here, i can do vf is equal to v -i plus at.

01:33 Vf is zero, v -i is 13 .28.

01:39 Acceleration is 9 .8, negative, and then t.

01:45 Okay, so let's see here.

01:54 Subtracting over negative 13 .28 equals negative 9 .8t and then dividing by negative 9 .8 on both sides gives us t is equal to what? so 13 .28 divided by 9 .8 is 1 .3 .3 .3 .3.

02:14 6 seconds.

02:18 All right, so how does that help us? well, we can fill this in on our table.

02:21 So 1 .36 seconds, 1 .36 seconds.

02:27 We want to know the initial velocity in the x.

02:30 So let's use one more equation to find that.

02:33 And we can use delta x is equal to vit plus 1 half a t square...