1
00:00:00,000 --> 00:00:00,580


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00:00:00,580 --> 00:00:02,900
Let's do a slightly
more complicated

3
00:00:02,900 --> 00:00:05,710
two-dimensional projectile
motion problem now.

4
00:00:05,710 --> 00:00:11,830
So in this situation, I am going
to launch the projectile off

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00:00:11,830 --> 00:00:12,470
of a platform.

6
00:00:12,470 --> 00:00:15,340


7
00:00:15,340 --> 00:00:17,660
And then it is going to
land on another platform.

8
00:00:17,660 --> 00:00:20,750


9
00:00:20,750 --> 00:00:27,190
And I'm going to fire the
projectile at an angle.

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00:00:27,190 --> 00:00:28,970
Let me draw this a
little bit better.

11
00:00:28,970 --> 00:00:30,460
So I'm going to
fire the projectile

12
00:00:30,460 --> 00:00:35,020
at an angle of-- let me
use a not so clean number.

13
00:00:35,020 --> 00:00:39,920
Let's say it is a
53-degree angle.

14
00:00:39,920 --> 00:00:43,720
And it's coming
out of the cannon.

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00:00:43,720 --> 00:00:45,960
And let me make it clear.

16
00:00:45,960 --> 00:00:49,100
So it's coming out--
let me do it this way,

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00:00:49,100 --> 00:00:50,880
just to make it 100% clear.

18
00:00:50,880 --> 00:00:53,720


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00:00:53,720 --> 00:00:56,660
So this angle right
over here is 53 degrees.

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00:00:56,660 --> 00:00:59,210


21
00:00:59,210 --> 00:01:01,650
And we are going
to have it come out

22
00:01:01,650 --> 00:01:07,110
of the muzzle of the cannon
with a velocity of 90

23
00:01:07,110 --> 00:01:07,860
meters per second.

24
00:01:07,860 --> 00:01:10,970


25
00:01:10,970 --> 00:01:13,430
And just to give ourselves
a sense of the heights,

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00:01:13,430 --> 00:01:16,630
or how high it's being
launched from-- so

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00:01:16,630 --> 00:01:19,420
from the muzzle of the
cannon down to here.

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00:01:19,420 --> 00:01:23,550
So this height right
over here, let's say

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00:01:23,550 --> 00:01:26,780
that that is 25 meters.

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00:01:26,780 --> 00:01:32,725
And let's say that this height
right over here is 9 meters.

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00:01:32,725 --> 00:01:34,986


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00:01:34,986 --> 00:01:36,610
And so we're essentially
launching this

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00:01:36,610 --> 00:01:38,140
from a height of 25 meters.

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00:01:38,140 --> 00:01:41,660
I know in the last video,
even though I drew the cannon

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00:01:41,660 --> 00:01:43,050
like this, we
assumed that it was

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00:01:43,050 --> 00:01:45,260
being launched from
an altitude of 0

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00:01:45,260 --> 00:01:47,930
and then landing back
at an altitude of 0.

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00:01:47,930 --> 00:01:50,380
Here we're assuming
we're launching it

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00:01:50,380 --> 00:01:52,300
from an altitude of 25
meters, because that's

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00:01:52,300 --> 00:01:54,281
when it's leaving the muzzle.

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00:01:54,281 --> 00:01:55,780
And it's going to
start decelerating

42
00:01:55,780 --> 00:01:57,196
at least in the
vertical direction

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00:01:57,196 --> 00:01:59,520
as soon as it leaves the muzzle.

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00:01:59,520 --> 00:02:01,470
And then we're
assuming it's not going

45
00:02:01,470 --> 00:02:03,020
to land back at
the same altitude.

46
00:02:03,020 --> 00:02:05,490
It's going to land at
a different altitude.

47
00:02:05,490 --> 00:02:07,839
So how do we think
about this problem?

48
00:02:07,839 --> 00:02:09,630
So the first thing
you'll always want to do

49
00:02:09,630 --> 00:02:13,370
is divide your velocity
vector into its horizontal

50
00:02:13,370 --> 00:02:14,770
and vertical components.

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00:02:14,770 --> 00:02:16,800
You use the vertical
component to figure out

52
00:02:16,800 --> 00:02:18,467
how long it's going
to stay in the air.

53
00:02:18,467 --> 00:02:20,800
And then you use the horizontal
component to figure out,

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00:02:20,800 --> 00:02:23,529
given how long it's in the
air, how far did it travel.

55
00:02:23,529 --> 00:02:25,070
And once again,
we're going to assume

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00:02:25,070 --> 00:02:28,120
that air resistance
is negligible.

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00:02:28,120 --> 00:02:30,280
So just based on what we
did in the last video--

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00:02:30,280 --> 00:02:35,740
and I'll go through all of the
steps in this one, as well.

59
00:02:35,740 --> 00:02:43,010
So if we draw our vector, the
length here is going to be 90.

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00:02:43,010 --> 00:02:44,430
This is our velocity vector.

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00:02:44,430 --> 00:02:47,320
The angle over here between
the x-axis and our vector

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00:02:47,320 --> 00:02:49,430
is 53 degrees.

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00:02:49,430 --> 00:02:51,970
And let me draw the
horizontal component.

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00:02:51,970 --> 00:02:54,330
The horizontal component
would look like this.

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00:02:54,330 --> 00:02:57,650
And the vertical component--
I'll do it in orange.

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00:02:57,650 --> 00:03:00,850
The vertical component would
look like-- that's not orange.

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00:03:00,850 --> 00:03:06,350
The vertical component
will look like this.

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00:03:06,350 --> 00:03:08,930
And so the vertical
component of the vector--

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00:03:08,930 --> 00:03:11,180
what would be the length of
this side right over here?

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00:03:11,180 --> 00:03:14,570
Well, this is the opposite side.

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00:03:14,570 --> 00:03:17,630
We know from basic
trigonometry sine

72
00:03:17,630 --> 00:03:20,780
of an angle is opposite
over the hypotenuse.

73
00:03:20,780 --> 00:03:27,490
So we know that the
sine of 53 degrees

74
00:03:27,490 --> 00:03:31,860
is equal to this
opposite side, is

75
00:03:31,860 --> 00:03:33,810
equal to the vertical velocity.

76
00:03:33,810 --> 00:03:41,350


77
00:03:41,350 --> 00:03:43,150
And I could write
it's the magnitude

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00:03:43,150 --> 00:03:44,556
of the vertical velocity.

79
00:03:44,556 --> 00:03:46,180
I write that subscript
y, because we're

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00:03:46,180 --> 00:03:47,360
in the y direction.

81
00:03:47,360 --> 00:03:50,230
That's the vertical
direction, over the length

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00:03:50,230 --> 00:03:53,020
of the hypotenuse,
over the magnitude

83
00:03:53,020 --> 00:03:54,810
of our original vector.

84
00:03:54,810 --> 00:03:58,930
Or we can get that this
side right over here.

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00:03:58,930 --> 00:04:01,370
If we multiply both
sides by 90, we

86
00:04:01,370 --> 00:04:03,670
get that the
magnitude of that side

87
00:04:03,670 --> 00:04:10,250
is going to be equal to 90
times the sine of 53 degrees.

88
00:04:10,250 --> 00:04:14,460


89
00:04:14,460 --> 00:04:18,190
Now, if we want to do
the horizontal component,

90
00:04:18,190 --> 00:04:20,700
the horizontal side
is adjacent to this.

91
00:04:20,700 --> 00:04:22,590
Cosine, soh cah toa.

92
00:04:22,590 --> 00:04:24,615
Cosine is adjacent
over hypotenuse.

93
00:04:24,615 --> 00:04:27,400


94
00:04:27,400 --> 00:04:33,180
So the horizontal
component of our velocity,

95
00:04:33,180 --> 00:04:39,580
I'll say in the x direction,
over the hypotenuse, over 90,

96
00:04:39,580 --> 00:04:46,060
is equal to the
cosine of 53 degrees.

97
00:04:46,060 --> 00:04:48,150
Cosine is adjacent
over hypotenuse.

98
00:04:48,150 --> 00:04:51,370
Adjacent, that's
this length, over 90.

99
00:04:51,370 --> 00:04:53,460
Multiply both sides by 90.

100
00:04:53,460 --> 00:04:57,440
You get that the
horizontal component

101
00:04:57,440 --> 00:05:02,705
is equal to 90 times
cosine of 53 degrees.

102
00:05:02,705 --> 00:05:07,970


103
00:05:07,970 --> 00:05:10,550
Now, how do we
figure out how long

104
00:05:10,550 --> 00:05:11,720
this thing stays in the air?

105
00:05:11,720 --> 00:05:13,770
Well, we'll use the
vertical component for that.

106
00:05:13,770 --> 00:05:16,680


107
00:05:16,680 --> 00:05:19,250
And especially since we're
dealing with different levels,

108
00:05:19,250 --> 00:05:22,460
we can't use that more basic
reasoning, that hey, whatever

109
00:05:22,460 --> 00:05:24,080
velocity we start
off at, it's going

110
00:05:24,080 --> 00:05:26,170
to be the same velocity but
in the opposite direction.

111
00:05:26,170 --> 00:05:27,390
Or the same magnitude
and velocity

112
00:05:27,390 --> 00:05:28,570
but the opposite direction.

113
00:05:28,570 --> 00:05:30,860
Because we're not going
to the same elevation.

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00:05:30,860 --> 00:05:33,630
But what we could do is
we can use the formula

115
00:05:33,630 --> 00:05:37,070
that we derived in
the previous video.

116
00:05:37,070 --> 00:05:39,360
That the displacement--
let me just copy and paste

117
00:05:39,360 --> 00:05:41,120
this a little bit
lower so we can use it.

118
00:05:41,120 --> 00:05:45,550


119
00:05:45,550 --> 00:05:47,500
So I'll stick it
right over here.

120
00:05:47,500 --> 00:05:49,240
So we could use this.

121
00:05:49,240 --> 00:05:52,286
We know that the displacement is
equal to the initial velocity--

122
00:05:52,286 --> 00:05:54,160
and we're dealing with
the vertical direction

123
00:05:54,160 --> 00:05:56,680
right here-- times the change
in time plus the acceleration,

124
00:05:56,680 --> 00:05:59,480
times the change in time
squared, divided by 2.

125
00:05:59,480 --> 00:06:02,354
So how do we use this to figure
out how long were in the air?

126
00:06:02,354 --> 00:06:03,520
So what is the displacement?

127
00:06:03,520 --> 00:06:07,370
If we're starting
at 25 meters high,

128
00:06:07,370 --> 00:06:09,840
and we're going
to 9 meters high.

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00:06:09,840 --> 00:06:13,740
So over the course, while
this thing is traveling,

130
00:06:13,740 --> 00:06:17,660
it will be displaced
downwards 16 meters.

131
00:06:17,660 --> 00:06:21,320


132
00:06:21,320 --> 00:06:23,360
Or another way to
think about it is

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00:06:23,360 --> 00:06:28,160
our displacement in
the vertical direction

134
00:06:28,160 --> 00:06:31,130
is going to be equal
to negative 16 meters.

135
00:06:31,130 --> 00:06:32,840
Let me write that a
little bit bigger.

136
00:06:32,840 --> 00:06:34,760
Negative 16 meters, right?

137
00:06:34,760 --> 00:06:38,200
Because 25 minus 9 is 16.

138
00:06:38,200 --> 00:06:42,060
And so we can put
that into the formula

139
00:06:42,060 --> 00:06:44,110
that we derived in
the previous video.

140
00:06:44,110 --> 00:06:47,920
We get negative 16-- I won't
write the units here just so

141
00:06:47,920 --> 00:06:52,680
that we don't take up
too much real estate,

142
00:06:52,680 --> 00:06:54,270
so that at least
it looks simple--

143
00:06:54,270 --> 00:06:56,404
is equal to the
initial velocity.

144
00:06:56,404 --> 00:06:58,570
We're dealing with just the
vertical dimension here.

145
00:06:58,570 --> 00:07:00,236
So we're just dealing
with the vertical.

146
00:07:00,236 --> 00:07:02,244


147
00:07:02,244 --> 00:07:04,410
And remember, it's negative
because our displacement

148
00:07:04,410 --> 00:07:05,560
is going to be downwards.

149
00:07:05,560 --> 00:07:08,170
We're losing altitude.

150
00:07:08,170 --> 00:07:10,610
So our vertical velocity--
we already figured that out.

151
00:07:10,610 --> 00:07:13,670
It is 90 times the
sine of 53 degrees.

152
00:07:13,670 --> 00:07:18,440


153
00:07:18,440 --> 00:07:21,109
Actually, let me do
it in that same color.

154
00:07:21,109 --> 00:07:22,900
The first time we do
a new type of problem,

155
00:07:22,900 --> 00:07:26,450
it's good to know-- so 90
times the sine of 53 degrees,

156
00:07:26,450 --> 00:07:33,230
times our change in time,
is equal to the acceleration

157
00:07:33,230 --> 00:07:36,980
of-- due to the force of gravity
for an object in free fall

158
00:07:36,980 --> 00:07:40,390
is going to be negative 9.8
meters per second squared.

159
00:07:40,390 --> 00:07:42,710
But we're dividing that by 2.

160
00:07:42,710 --> 00:07:50,020
So we're going to have minus 4.9
meters per second squared times

161
00:07:50,020 --> 00:07:50,956
delta t squared.

162
00:07:50,956 --> 00:07:52,330
Times our change
in time squared.

163
00:07:52,330 --> 00:07:56,670


164
00:07:56,670 --> 00:07:58,660
So how do we solve
something like this?

165
00:07:58,660 --> 00:08:00,530
You can't just factor
out a t and solve it.

166
00:08:00,530 --> 00:08:03,200
But you might recognize
this is a quadratic equation

167
00:08:03,200 --> 00:08:03,880
right over here.

168
00:08:03,880 --> 00:08:05,588
And the way you solve
quadratic equations

169
00:08:05,588 --> 00:08:09,230
is you get everything onto
one side of this equation.

170
00:08:09,230 --> 00:08:11,320
And then you either
factor it out.

171
00:08:11,320 --> 00:08:12,870
But more likely
in this situation,

172
00:08:12,870 --> 00:08:14,810
we will use the
quadratic formula,

173
00:08:14,810 --> 00:08:16,630
which we've proved
in other videos

174
00:08:16,630 --> 00:08:20,250
and hopefully given you the
intuition for it-- to actually

175
00:08:20,250 --> 00:08:22,869
solve for the times where
your elevation, where

176
00:08:22,869 --> 00:08:24,660
your displacement in
the vertical direction

177
00:08:24,660 --> 00:08:26,430
is negative 16 meters.

178
00:08:26,430 --> 00:08:28,250
And you'll get two
solutions here.

179
00:08:28,250 --> 00:08:30,940
And one of the solutions will
be a negative change in time.

180
00:08:30,940 --> 00:08:33,580
So it'll be like at
sometime in the past,

181
00:08:33,580 --> 00:08:35,500
you were also at
negative 16 meters.

182
00:08:35,500 --> 00:08:37,280
That's nonsensical
for this problem.

183
00:08:37,280 --> 00:08:40,440
So we'll want to take
the positive value here.

184
00:08:40,440 --> 00:08:46,250
So let's put all of this on
one side of the equation.

185
00:08:46,250 --> 00:08:47,845
So let's add 16 to both sides.

186
00:08:47,845 --> 00:08:50,790


187
00:08:50,790 --> 00:08:54,230
On the left-hand side,
you just get a 0.

188
00:08:54,230 --> 00:08:55,871
0 is equal to--
and I'll write it

189
00:08:55,871 --> 00:08:58,370
in kind of the traditional way
that we're used to seeing it.

190
00:08:58,370 --> 00:09:00,078
I'll write the highest
degree term first.

191
00:09:00,078 --> 00:09:03,435
So negative 4.9 times
delta t squared.

192
00:09:03,435 --> 00:09:06,570


193
00:09:06,570 --> 00:09:25,320
And then we have plus 90 sine
of 53 degrees times delta t,

194
00:09:25,320 --> 00:09:26,335
and then plus 16.

195
00:09:26,335 --> 00:09:28,850


196
00:09:28,850 --> 00:09:32,170
I'm going to do that in yellow.

197
00:09:32,170 --> 00:09:35,406
All of this is equal to 0.

198
00:09:35,406 --> 00:09:37,530
And this, once again, is
just a quadratic equation.

199
00:09:37,530 --> 00:09:39,560
We can find its roots.

200
00:09:39,560 --> 00:09:41,400
And the roots will be
in terms of delta t.

201
00:09:41,400 --> 00:09:45,030
We can solve for delta t
using the quadratic formula.

202
00:09:45,030 --> 00:09:50,540
So we get delta t-- and if
this is very unfamiliar to you,

203
00:09:50,540 --> 00:09:53,570
review the videos on Khan
Academy in the algebra playlist

204
00:09:53,570 --> 00:09:54,630
on the quadratic formula.

205
00:09:54,630 --> 00:09:55,550
And if you don't know
where it came from,

206
00:09:55,550 --> 00:09:57,210
we also prove it for you.

207
00:09:57,210 --> 00:10:00,950
So it's equal to negative B.
B is this term right here,

208
00:10:00,950 --> 00:10:03,000
the coefficient on the delta t.

209
00:10:03,000 --> 00:10:07,844
So it's going to be negative
90 sine of 53 degrees.

210
00:10:07,844 --> 00:10:09,510
I'll write the quadratic
formula up here

211
00:10:09,510 --> 00:10:12,870
for those of you who
don't fully remember it.

212
00:10:12,870 --> 00:10:16,750
So if I'm trying to
solve Ax squared plus Bx

213
00:10:16,750 --> 00:10:20,050
plus C is equal to 0,
the roots over here

214
00:10:20,050 --> 00:10:24,600
are going to be negative B plus
or minus the square root of B

215
00:10:24,600 --> 00:10:31,940
squared minus 4AC, all
of that over 2 times A.

216
00:10:31,940 --> 00:10:33,700
These are going to
be the x values that

217
00:10:33,700 --> 00:10:36,114
satisfy this equation up here.

218
00:10:36,114 --> 00:10:37,530
So that's all I'm
doing over here.

219
00:10:37,530 --> 00:10:38,660
This is the B value.

220
00:10:38,660 --> 00:10:43,159
Negative B plus or
minus-- and it's

221
00:10:43,159 --> 00:10:45,450
going to turn out that we
only care about the plus one,

222
00:10:45,450 --> 00:10:47,590
because that's going to
give us the positive value.

223
00:10:47,590 --> 00:10:48,923
But I'll just write it out here.

224
00:10:48,923 --> 00:10:53,810
Plus or minus the square
root of B squared.

225
00:10:53,810 --> 00:10:56,060
So it's this quantity squared.

226
00:10:56,060 --> 00:11:03,610
So it is 90 sine of 53
degrees squared, minus 4--

227
00:11:03,610 --> 00:11:05,770
we're going to run
[? out that ?] little space.

228
00:11:05,770 --> 00:11:16,120
So minus 4 times A,
which is negative 4.9.

229
00:11:16,120 --> 00:11:21,130
Well, let me just write negative
4.9 times C. C over here

230
00:11:21,130 --> 00:11:23,065
is 16, times 16.

231
00:11:23,065 --> 00:11:25,350
Let me put this radical
all the way over here.

232
00:11:25,350 --> 00:11:26,720
All of that over 2A.

233
00:11:26,720 --> 00:11:30,360


234
00:11:30,360 --> 00:11:32,600
So A is negative 4.9.

235
00:11:32,600 --> 00:11:37,800
2 times A is negative 9.8.

236
00:11:37,800 --> 00:11:40,110
So now we can get
the calculator out

237
00:11:40,110 --> 00:11:41,604
to figure out our
change in time.

238
00:11:41,604 --> 00:11:44,020
And I'm just going to focus
on the positive version of it.

239
00:11:44,020 --> 00:11:45,810
I'll leave it up to you to
find the negative version

240
00:11:45,810 --> 00:11:48,101
and see that it'll give you
a negative value for change

241
00:11:48,101 --> 00:11:48,690
in time.

242
00:11:48,690 --> 00:11:50,370
And that's
nonsensical, so we only

243
00:11:50,370 --> 00:11:52,080
care about the
positive change in time

244
00:11:52,080 --> 00:11:58,290
where we get to a displacement
of negative 16 meters.

245
00:11:58,290 --> 00:12:00,470
Let's get the calculator out.

246
00:12:00,470 --> 00:12:03,770
So we get-- want to
do this carefully.

247
00:12:03,770 --> 00:12:09,809
We have negative 90
sine of 53 degrees plus.

248
00:12:09,809 --> 00:12:12,100
I'm doing the plus version
here because that'll give us

249
00:12:12,100 --> 00:12:17,320
the positive value--
plus the square root of.

250
00:12:17,320 --> 00:12:18,680
And I'll do this in parentheses.

251
00:12:18,680 --> 00:12:23,730
90 sine of 53 degrees squared.

252
00:12:23,730 --> 00:12:25,400
That's that part right there.

253
00:12:25,400 --> 00:12:26,830
These two negatives cancel out.

254
00:12:26,830 --> 00:12:29,840
So I could say this is
plus 4 times positive 4.9.

255
00:12:29,840 --> 00:12:37,450
So plus 4 times 4.9 times 16.

256
00:12:37,450 --> 00:12:40,630
And then that closes
off our entire radical.

257
00:12:40,630 --> 00:12:43,710
And so this will give me
the numerator up here.

258
00:12:43,710 --> 00:12:44,900
That gives me the numerator.

259
00:12:44,900 --> 00:12:53,580
And then I want to divide that
by-- did I do the negative 90?

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00:12:53,580 --> 00:12:55,710
Oh, and I just realized
that I made a mistake.

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00:12:55,710 --> 00:12:59,240
I said that the positive
version would give you

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00:12:59,240 --> 00:13:00,040
the positive time.

263
00:13:00,040 --> 00:13:01,373
But now we realize that's wrong.

264
00:13:01,373 --> 00:13:03,960
Because when I took the positive
version, when I put a plus up

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00:13:03,960 --> 00:13:07,960
here, I get a positive
2.14 for the numerator.

266
00:13:07,960 --> 00:13:10,810
But then we divide
it by negative 9.8.

267
00:13:10,810 --> 00:13:12,310
We're going to get
a negative value.

268
00:13:12,310 --> 00:13:14,560
So that's not going to be
the time that we care about.

269
00:13:14,560 --> 00:13:16,950
We care about the time where
this is a negative value.

270
00:13:16,950 --> 00:13:19,340
So let me re-enter that.

271
00:13:19,340 --> 00:13:20,860
So let me do the negative value.

272
00:13:20,860 --> 00:13:24,580
So let me move
back a little bit.

273
00:13:24,580 --> 00:13:31,979
And then let me replace
this with a minus sign.

274
00:13:31,979 --> 00:13:33,770
So I'm going to look
at the negative value,

275
00:13:33,770 --> 00:13:35,660
because I want
the positive time.

276
00:13:35,660 --> 00:13:38,559
And so now my numerator
here is a negative value.

277
00:13:38,559 --> 00:13:40,350
And so this is actually
what we care about.

278
00:13:40,350 --> 00:13:42,850
We care about the
numerator's a negative value.

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00:13:42,850 --> 00:13:49,760
You divide by
negative 9.8, and you

280
00:13:49,760 --> 00:13:55,530
get 14.8-- I'll just
round-- 14.89 seconds.

281
00:13:55,530 --> 00:13:58,500
So delta t, the
positive version,

282
00:13:58,500 --> 00:14:01,920
is equal to 14.89 seconds.

283
00:14:01,920 --> 00:14:05,832
And so my initial comment about
using the positive version

284
00:14:05,832 --> 00:14:08,290
was wrong because we have this
denominator that's negative.

285
00:14:08,290 --> 00:14:10,640
So you want the
numerator to be negative.

286
00:14:10,640 --> 00:14:12,370
And only when the
numerator is negative

287
00:14:12,370 --> 00:14:14,520
will the whole
expression be positive.

288
00:14:14,520 --> 00:14:18,052
And so we got this positive
time of 14.89 seconds.

289
00:14:18,052 --> 00:14:19,260
I'm going to leave you there.

290
00:14:19,260 --> 00:14:21,094
And the next part of
the video-- actually, I

291
00:14:21,094 --> 00:14:23,509
might as well just solve it
instead of making a new video.

292
00:14:23,509 --> 00:14:24,960
Although this is running long.

293
00:14:24,960 --> 00:14:31,800
So the amount of time that we're
in the air is 14.89 seconds.

294
00:14:31,800 --> 00:14:36,192
So if I were to ask you the
horizontal displacement,

295
00:14:36,192 --> 00:14:37,650
it's going to be
the amount of time

296
00:14:37,650 --> 00:14:42,130
we're in the air times your
constant horizontal velocity.

297
00:14:42,130 --> 00:14:45,090
And we already figured out our
constant horizontal velocity.

298
00:14:45,090 --> 00:14:49,700
So if you want to figure
out how far along the x-axis

299
00:14:49,700 --> 00:14:54,210
we get displaced, we
just take this time

300
00:14:54,210 --> 00:14:57,730
times-- that just means
our previous answer--

301
00:14:57,730 --> 00:15:04,050
times this value right here,
times 90 cosine of 53 degrees.

302
00:15:04,050 --> 00:15:06,760
And that gives 806 meters.

303
00:15:06,760 --> 00:15:11,323
So this displacement right
over here is 806 meters.

304
00:15:11,323 --> 00:00:00,000