Free Fall Physics Problems - Acceleration Due To Gravity - Free Educational videos for Students in K-12

Free Fall Physics Problems - Acceleration Due To Gravity - By The Organic Chemistry Tutor

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00:01	let's see if you hold two balls in the air
00:05	, A 10 g Metal Ball And a five g
00:09	metal ball And you hold it five ft above the
00:13	ground , so they're at the same height . Once
00:18	you release it from rest , both balls will be
00:21	in free fall . Which one will hit the ground
00:25	first ? Is it the 10 grand ball Or is
00:28	it the five grandpa ? Both objects will reach the
00:34	ground at the same time ? The reason for that
00:38	, their place at the same height and are under
00:41	the influence of the same gravity , Earth's gravity .
00:45	The acceleration due to gravity is 9.8 m per second
00:49	squared , which we'll talk more about that later .
00:53	But because everything is the same , the height is
00:55	the same , The acceleration is the same . If
00:58	you take away a resistance , both objects will hit
01:01	the ground . Now , let's say if we use
01:07	an actual demonstration of a brick versus a flat piece
01:13	of paper . So the brick is a lot heavier
01:18	than the flat piece of paper , let's say it's
01:20	a A one kg Brick . Now , with a
01:28	resistance , which one will hit the ground first ,
01:32	the brick is going to go straight down the paper
01:35	might go this way , they might go that way
01:37	and then eventually fall to the ground because of air
01:40	resistance . Now , what's going to happen if you
01:45	take the same brick , but you crumpled up the
01:48	paper so that it's very , very small , You
01:52	take the same paper and crumple it up . Now
01:55	the effects of a resistance on this paper will be
01:57	greatly reduced . If you crumple up the paper very
02:01	tightly and you let it go , these two will
02:04	hit the ground approximately about the same time . The
02:08	greater the surface area of the paper , the greater
02:12	the effect of a resistance . A resistance increases with
02:15	surface area . So once you crumpled up the paper
02:17	and then you drop it , you'll see that it's
02:20	about the same time when it reaches the ground with
02:23	a brick , the air resistance is greatly reduced .
02:27	So if you can eliminate a resistance completely , then
02:30	both objects should hit the ground at the exact same
02:33	time because they're under the influence of the same gravity
02:37	, Earth's gravitational field . Now let's talk more about
02:43	the acceleration due to gravity . So if we have
02:46	a bar and if we release it from rest ,
02:48	it's going to fall down And it's going to accelerate
02:52	at the rate of 9.8 m/s squared . So if
02:56	you recall , acceleration tells you how fast the velocity
03:00	is changing every second , So initially the speed might
03:05	be zero one second later The velocity is going to
03:12	be negative . 9.8 . The speed is just positive
03:17	. My point speed is always positive , but velocity
03:20	can be positive or negative depending on the direction .
03:24	So because the ball is going in a negative Y
03:27	direction , the velocity is negative . Now technically acceleration
03:33	is negative 9.8 m/s squared because the object is going
03:37	to accelerate in the negative Y direction , gravity pulls
03:40	things down , not up . Now . two seconds
03:44	later , The velocity is going to be negative 19.6
03:50	m/s . So every second the velocity is changing ,
03:55	the speed changes every Every second . The speed changes
03:58	by 9.8 . So as the ball drops notice that
04:06	the velocity is decreasing by nine point it's becoming more
04:10	and more negative . The speed , however , is
04:12	increasing . Keep in mind , speed is positive .
04:15	So at this point the speed is positive , my
04:17	.8 it's 19.6 And here it's positive 29.4 . So
04:24	, an object in free fall That's under the influence
04:27	of gravity , the speed is increasing by 9.8 every
04:30	second . But the velocity because it's negative , is
04:33	decreasing by 9.8 every second . So remember acceleration ,
04:38	tells you how fast the velocity is changing every second
04:42	. Now . Before we go over a few freefall
04:46	problems , we need to talk about the equations that
04:49	you need to solve them . So whenever an object
04:52	is moving with constant speed , this is the equation
04:55	that you need to use . D . Is equal
04:57	to eating . D can be used as distance or
05:00	displacement . Just remember ? Distance is the scale of
05:03	quantity , displacement is a vector , so displacement can
05:07	be positive or negative , but distance is always positive
05:12	. So any time an object is moving with constant
05:14	speaker , you can use this equation . Now .
05:16	When an object is moving with constant acceleration , you
05:20	can use any one of these four equations . The
05:23	final is equal to the initial plus 18 . The
05:27	final could represent the final speed or final velocity .
05:31	The initial is the initial speed or initial velocity .
05:34	A . Is the acceleration T . Is the time
05:37	. So you may see me use the word speed
05:40	and velocity interchangeably . Just remember that velocity is speed
05:47	with direction . Speed is the scale of quantity .
05:49	It can only be positive . Velocity can be positive
05:52	or negative depending on what direction you're going . So
05:56	for an object that's moving to the right , the
05:58	velocity is positive . If the object moves to the
06:01	left the velocity is negative . But in freefall situations
06:05	we're dealing with motion in the Y direction . When
06:08	an object goes up , the velocity is positive .
06:11	When it goes down the velocity is negative . The
06:22	next formula that you need to know Is this one
06:25	D . is equal to the initial T plus one
06:29	half at squared And then there's this one d .
06:34	is equal to 1/2 the initial plus the final times
06:39	T . And the final squared is equal to v
06:44	. Initial squared plus two A . D . So
06:47	there are five formulas that you need to know .
06:50	So vehstree plus this one and this equation only when
06:58	an object is moving at constant speed , when it's
07:01	moving with constant acceleration , you can use these four
07:04	equations . So let's start with this problem , A
07:09	ball is dropped from rest on a cliff . What
07:12	is the speed of the ball five seconds later ?
07:15	So let's say this is the cliff and here is
07:20	the ball so it falls down . But we don't
07:24	know if it hits the ground at this point .
07:27	We just want to find the speed five seconds later
07:34	. So it's important to make a list of what
07:37	you have and the variable they need to find what
07:42	is the initial speed of the ball on this problem
07:46	notice that the ball is dropped from rest so the
07:49	initial speed is zero . Our goal is to find
07:53	the final speed . Now we know the time ,
07:58	The time is five seconds and the acceleration Due to
08:03	gravity is -9.8 . The acceleration due to gravity is
08:08	in a negative Y direction , so that's why it's
08:10	negative . So what equation that was listed earlier ?
08:15	Has these four variables ? The equation that we need
08:20	is this one v final is equal to v initial
08:23	plus 80 . The initial is zero . The acceleration
08:29	is negative 9.8 & T is five , So negative
08:35	9.8 times five is -45 . I mean not 45
08:39	but 49 . So now Let's go back to the
08:48	question , what is the speed of the ball ?
08:51	five seconds later . Nothing about your answer . The
08:56	answer . The speed Is positive . 49 m/s .
09:02	Remember speed cannot be negative so you gotta make it
09:06	positive . So this is the answer for part time
09:10	. Now , part B . What is the velocity
09:12	of the ball at this time ? The velocity is
09:15	negative ? So that's the velocity right there . It's
09:18	negative 49 m/s because the ball is moving in a
09:22	negative y direction , velocity is negative . Remember velocity
09:26	is a vector quantity . Speed is scalar . Now
09:31	let's move on to part , see how far does
09:34	it travel during this time ? What equation do you
09:40	think ? We need to use ? One equation that
09:46	can help us define it ? Is this one D
09:48	. Is equal to v . Initial T plus one
09:51	half 80 square . We already have the initial speed
09:55	. we know the time and we have the acceleration
09:57	. So we have enough information to use this equation
10:01	. So the initial is zero zero times T .
10:03	is just going to be zero Acceleration is negative 9.8
10:08	& T is five , So half of negative 9.8
10:13	, That's negative 4.9 . If you multiply that by
10:16	five squared , That will give you a value of
10:20	negative 122.5 m now , what does this answer represent
10:29	? That answer is not the distance traveled , but
10:32	rather it's the displacement . This is the answer for
10:35	part D . Remember displacement is a vector like velocity
10:39	. It can be negative or positive because the object
10:42	moves in the negative Y direction . The displacement is
10:45	negative . But to answer part , see how far
10:48	does it travel during this time ? Part C is
10:51	not looking for the displacement is looking for the distance
10:53	traveled . The distance is simply positive . 122.5 whenever
11:02	an object moves in one direction , if it doesn't
11:05	change direction , if it moves straight the distance and
11:08	displacement , they have the same value . They have
11:12	the same magnitude , but the signs may be different
11:15	depending on what direction is going . But any time
11:19	you have an object that's moving in a straight line
11:22	, the distance and displacement have the same numerical value
11:26	, just as signs might be different . So that's
11:28	it for this problem , Number two , A ball
11:33	is thrown downward at an initial speed of 15 m/s
11:37	from the top of a cliff . What is the
11:40	speed and velocity of the ball eight seconds later .
11:46	So this problem is similar to the last problem .
11:49	Only one key difference . The ball is not released
11:53	from rest . Rather , it strode down with an
11:57	initial speed , and that initial speed Is 15 m/s
12:03	. But let's use the initial velocity when dealing with
12:06	this equation . So we're going to use a negative
12:09	15 m/s because it's going in a negative y direction
12:14	. Our goal is to find the speed and velocity
12:17	eight seconds later . So we need to find the
12:20	final velocity . The time is eight seconds and the
12:24	acceleration is still negative 9.8 . So let's use the
12:30	same equation to find the final velocity . So the
12:35	initial velocity is negative 15 Plus the acceleration of negative
12:40	9.8 , multiplied by the time of eight seconds ,
12:45	-9.8 times eight . That's negative 78.4 , So negative
12:53	15 plus negative 78.4 , that's -93.4 m/s . So
13:08	this is the final velocity eight seconds later . The
13:12	speed eight seconds later is simply positive , 93.4 .
13:17	That's what you just got to change the sign .
13:21	Just remember . Speed is always positive . Now let's
13:27	find the displacement and also the distance that it travels
13:32	. So let's use the same equation as the first
13:35	example . So D . Is equal to the initial
13:37	T . Plus one half a T squared . So
13:42	the initial this time is negative 15 And he is
13:47	eight . The acceleration , It's negative 9.8 and we're
13:53	going to plug in 8 40 again , it's negative
13:59	15 times eight . That's negative 1 20 Half of
14:03	negative 9.8 is -4.9 . So negative 4.9 times eight
14:09	squared . That's a -313.6 . So when adding these
14:17	two together , You should get negative 433.6 m .
14:24	So this is the displacement of the ball During these
14:30	eight seconds . Now , the distance that it travels
14:33	is positive , 400 and 33 0.6 m . So
14:45	that's the distance that it travels . All you need
14:48	to do is just make the answer positive . Number
14:54	three , A stone is dropped from the top of
14:57	the building and hits the ground five seconds later .
15:00	How tall is the building ? So let's start with
15:04	a picture . So let's say that's the building and
15:11	the stone is dropped from the top of a building
15:13	. Our goal is to find the height of the
15:17	building . The height of the building is basically the
15:23	distance at the ball travels until it hits the ground
15:26	. So if we could find the distance that it
15:28	travels , we could find the height of the building
15:31	. Now , what equation should we use in order
15:35	to find out which equation to use ? We need
15:38	to make a list of everything that we have now
15:43	. It didn't say the stone is thrown down ,
15:47	so therefore if the stone is dropped from the top
15:50	of a building , we know it's dropped from rest
15:52	, which means the initial speed . Is there a
15:55	? We don't know what the final speed is ,
15:58	but we do have the time and we know the
16:00	acceleration for any object in free fall and the object
16:05	that's fallen under the influence of gravity . This acceleration
16:09	will always be the same value in the y direction
16:14	. So our goal is to find D . In
16:16	the Y direction , which is the same as the
16:18	hype . So once again we could use this equation
16:21	. Dean is equal to venus Schulte plus one half
16:25	a T . Squared . But because the initial is
16:29	zero , we don't need this portion of the equation
16:32	, so therefore the height of the building , which
16:35	we can replace with the displacement . The height of
16:38	the building is going to be just one half a
16:40	. T squared . For those of you who just
16:43	want a simple formula to find this answer . But
16:48	I'm going to use A . D . In this
16:49	example , A is negative 9.8 T . Is five
16:59	. So negative 4.9 , Which is half of 9.8
17:02	times five square . That's -1 22.5 m . So
17:09	keep in mind that's the displacement of the ball .
17:12	So what that means is that the ball Travels 122.5
17:17	m down before hits the ground . So therefore the
17:21	height of the building is the same . But you
17:25	don't need to describe the height of the building using
17:28	a negative number . All you need to say is
17:31	is that the building is 122.5 m tall . You
17:36	don't have to say -122.5 . That's not gonna make
17:38	any sense . So this is the height of the
17:40	building . So now that you know how to do
17:44	the last problem , Go ahead and try this one
17:49	. A stone is thrown downwards from the top of
17:51	a cliff at 24m/s and hits the ground seven seconds
17:55	later . How tall is the cliff ? So it's
18:02	no longer release from response . Someone just strolls it
18:05	down . So therefore , we know that this is
18:08	an initial speed Which is 24 , but we're going
18:11	to use the initial velocity Which is negative 24 m/s
18:16	. We have the time it takes for it to
18:18	hit the ground . That's seven seconds . The acceleration
18:21	in the Y direction is still negative 9.8 m per
18:25	second squared . Our goal is to find the height
18:28	of the cliff . It's basically we just need to
18:31	find the displacement of the ball . So let's use
18:35	the same form of D . Is equal to the
18:37	initial T . Plus one half 80 square . This
18:41	time we need this portion of the equation . So
18:45	the initial is -24 T . S . Seven A
18:51	. Is the same . And now let's go ahead
18:53	and funny answer -24 times seven . That's negative 1
19:01	68 And -4.9 times seven squared . That's about -2
19:12	40.1 . So the displacement of the ball is -408.1
19:23	m . So what this means is that the ball
19:26	travels 408.1 m in a negative y direction . That's
19:30	why it's negative . But the distance traveled , which
19:34	is the height of the cliff , that's positive 408.1
19:39	m and that's the answer . A rock is released
19:46	from rest on a 700 m building . How long
19:50	does it take to hit the ground ? What is
19:52	the speed and velocity of the ball just before it
19:55	hits the ground ? Well , let's start with the
19:57	picture . So this time were given the height of
20:02	the building and initially we need to find out how
20:07	long does it take to hit the ground . So
20:10	we got to find the time . Let's make a
20:12	list of what we have . The rock is released
20:15	from rest , so the initial speed is zero .
20:18	We have the acceleration in the Y direction . That's
20:21	negative 9.8 we're looking for the time , but we
20:30	do have the displacement . The displacement in the Y
20:33	direction is not positive 700 , But it's a negative
20:38	700 because the ball is moving in the negative Y
20:43	direction . So let's use this equation D . Is
20:47	equal to the initial T . Plus 1/2 a .
20:52	T . Now d . is negative 700 . The
20:59	initial Fortunately zero . So we can avoid using the
21:02	quadratic equation . The acceleration Is negative 9.8 . So
21:08	now all we gotta do is find T . So
21:11	half of 9.8 is 4.9 Not to isolate T Square
21:17	list of I both sides by -4.9 . So negative
21:25	700 , Divided by negative 4.9 Is 142 0.86 and
21:34	it's positive . So now let's take the square root
21:37	of both sides . So t . I'm going to
21:44	write it right here Is 11.95 seconds . So that's
21:49	how long it takes for the rock to hit the
21:54	ground . Now , what about part B . How
22:04	can we find the speed and velocity of the ball
22:08	just before hits the ground ? So we're looking for
22:16	VF . In this case we have the initial speed
22:21	, we have the acceleration and we have the time
22:24	. So therefore we can use this familiar equation .
22:28	The final is equal to the initial plus 80 ,
22:32	so the initial A . Is zero . The acceleration
22:37	Is negative 9.8 and we now have the time ,
22:41	which is 11.95 seconds , -9.8 times 11.95 . That's
22:54	negative 117 0.1 meters per second . So this is
23:00	the velocity of the wall just before it hits the
23:03	ground . The speed of the ball before it hits
23:06	the ground . It's the same number but positive ,
23:10	It's positive 1 17.1 meters per second . So these
23:16	are the two answers . It's a part being .

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