00:01
Hello and welcome to problem 56.
00:04
If you've ever thought to yourself, you wish you could do a problem that had about 8 ,000 parts to it, then 56 is the right problem for you.
00:11
So in this problem, we have a golf ball that is dropped from 9 .5 meters in the air.
00:17
It hits the ground and bounces up to a height of 5 .7 meters before it falls 4 .5 meters towards the ground where it is caught.
00:27
And this question wants to know how long does this golf ball actually spend in the air? since there's three different parts of this golf ball's motion, we need to do at least three different kinematic calculations to figure that out.
00:41
So a few things i want to set up here.
00:43
I'm going to draw a little sketch of what's actually happening for this one.
00:47
Here's my golf ball.
00:49
Phase one is the golf ball falling to the ground.
00:54
It then hits the ground and bounces back upwards for, phase two, to some height that's not quite as tall as it started at.
01:04
It then falls down towards the ground to its ending point right about here.
01:10
Now, since most of the motions are pointing downwards, since most of my displacements are going downwards, and because acceleration is going downwards, i'm going to define my directions as anything in the downward direction is going to be positive, and anything that is upwards is going to be negative.
01:29
Now, if you, you solved this problem and just switch that around and went the other way, you'd end up with the exact same answers we're going to get.
01:37
But because there's so much more downwards motion in this problem, it's going to reduce the difficulty, or at least the irritation level of these problems a considerable bit, to call downwards the positive direction.
01:48
So with that, and i'm going to keep my color coding here for which section we're in, let's talk about the motion during part one.
01:55
We know the initial velocity is zero meters per second when it is dropped.
01:59
We also know we're on earth, so our acceleration is 9 .8 meters per second squared downwards, which is my positive direction.
02:07
And we know it's going to fall 9 .5 meters down, which again, the positive direction before it hits the ground.
02:15
Now, my goal here is to figure out how long it spends in the air, so i want to know t.
02:20
Now, that means i know my four variables there, or i know three of them, rather, and i'm looking for the fourth.
02:26
The final velocity is the variable i don't know and don't want to know.
02:30
So when i'm picking which equation to use, i'm just looking for the equation that does not have that final velocity in it.
02:36
So to solve this, we start with x equals v0 t plus one half a t squared.
02:43
I'm going to get my helpful little diagram here out of the middle, so we have some room to actually solve this.
02:50
So, do this again, x equals v not t plus one half a t squared.
03:01
When i plug in my numbers for this first one, we have my distance of 9 .5 is equal to v .0 t, which since my initial velocity is zero, that whole term goes to zero, plus 4 .9t squared.
03:16
Then that gives me a t squared value of 1 .94 and a t value of 1 .39.
03:27
Now that's just the time for part one of this problem.
03:31
My goal is to figure out how long it'll take to do all three parts.
03:34
But hey, we're one -third of the way there.
03:37
So i'm going to tuck this off to the side.
03:40
And let's do the same thing again, but analyzing the second piece of the motion instead of the first one.
03:46
So the second one has a few things that are a little bit different.
03:49
First of all, we know its final velocity because it's bouncing upwards...