1
00:00:00,000 --> 00:00:00,311


2
00:00:00,311 --> 00:00:02,560
In the last video, I told
you that we would figure out

3
00:00:02,560 --> 00:00:05,580
the final velocity of
when this thing lands.

4
00:00:05,580 --> 00:00:06,400
So let's do that.

5
00:00:06,400 --> 00:00:08,570
I forgot to do it
in the last video.

6
00:00:08,570 --> 00:00:10,460
So let's figure out
the final velocity--

7
00:00:10,460 --> 00:00:12,320
the vertical and the
horizontal components

8
00:00:12,320 --> 00:00:13,730
of that final velocity.

9
00:00:13,730 --> 00:00:16,950
And then we can reconstruct
the total final velocity.

10
00:00:16,950 --> 00:00:18,710
So the horizontal
component is easy,

11
00:00:18,710 --> 00:00:20,918
because we already know that
the horizontal component

12
00:00:20,918 --> 00:00:23,975
of its velocity is this value
right over here, which we--

13
00:00:23,975 --> 00:00:26,060
this 30 cosine of 80 degrees.

14
00:00:26,060 --> 00:00:28,270
And that's not going to
change at any point in time.

15
00:00:28,270 --> 00:00:32,119
So this is going to be
the horizontal component

16
00:00:32,119 --> 00:00:35,381
of the projectile's
velocity when it lands.

17
00:00:35,381 --> 00:00:36,880
But what we need
to do is figure out

18
00:00:36,880 --> 00:00:40,310
the vertical component
of its velocity.

19
00:00:40,310 --> 00:00:42,950
Well, one thing we did
figure out in the last video,

20
00:00:42,950 --> 00:00:47,260
we figured out what the time
in the air is going to be.

21
00:00:47,260 --> 00:00:50,970
And we know a way of figuring
out our final velocity

22
00:00:50,970 --> 00:00:55,580
from an initial velocity
given our time in the air.

23
00:00:55,580 --> 00:00:58,127
We know that a
change in velocity --

24
00:00:58,127 --> 00:00:59,960
and we're only dealing
in the vertical now--

25
00:00:59,960 --> 00:01:01,501
we're only dealing
with the vertical,

26
00:01:01,501 --> 00:01:04,730
because the horizontal velocity
is not going to change.

27
00:01:04,730 --> 00:01:07,290
We've assumed that air
resistance is negligible.

28
00:01:07,290 --> 00:01:09,690
So we're only dealing with
the vertical component

29
00:01:09,690 --> 00:01:10,450
right over here.

30
00:01:10,450 --> 00:01:13,210


31
00:01:13,210 --> 00:01:15,680
We know that the
change in velocity--

32
00:01:15,680 --> 00:01:17,340
or, we could say
the horizontal--

33
00:01:17,340 --> 00:01:21,770
the vertical component of
the change in velocity,

34
00:01:21,770 --> 00:01:28,680
is equal to the vertical
component of the acceleration

35
00:01:28,680 --> 00:01:30,430
times time.

36
00:01:30,430 --> 00:01:31,930
Now, we know what
the change in time

37
00:01:31,930 --> 00:01:35,810
is, we know it is-- I'll just
write down times our time.

38
00:01:35,810 --> 00:01:40,250
And what is our
change in velocity?

39
00:01:40,250 --> 00:01:45,490
Well, our change in velocity
is our final vertical velocity

40
00:01:45,490 --> 00:01:47,894
minus our initial
vertical velocity.

41
00:01:47,894 --> 00:01:49,810
And we know what our
initial vertical velocity

42
00:01:49,810 --> 00:01:51,160
is, we solved for it.

43
00:01:51,160 --> 00:01:53,860
Our initial vertical
velocity, we figured out,

44
00:01:53,860 --> 00:01:56,800
was 29.54 meters per second.

45
00:01:56,800 --> 00:02:02,220
That's 30 sine of 80 degrees,
29.54 meters per second.

46
00:02:02,220 --> 00:02:08,190
So this is going to be minus
29.54 meters per second,

47
00:02:08,190 --> 00:02:11,540
is equal to-- our acceleration
in the vertical direction

48
00:02:11,540 --> 00:02:14,400
is negative, because
it's accelerating us

49
00:02:14,400 --> 00:02:18,830
downwards, negative 9.8
meters per second squared.

50
00:02:18,830 --> 00:02:21,860
And our time in the
air is 5.67 seconds.

51
00:02:21,860 --> 00:02:25,460
Times 5.67 seconds.

52
00:02:25,460 --> 00:02:27,840
And so we can solve for
the vertical component

53
00:02:27,840 --> 00:02:29,610
of our final velocity.

54
00:02:29,610 --> 00:02:31,830
So once again, this is
the vertical component.

55
00:02:31,830 --> 00:02:33,360
This isn't the total one.

56
00:02:33,360 --> 00:02:35,060
So, the vertical component.

57
00:02:35,060 --> 00:02:36,884
Let me-- well I wrote
vertical up here.

58
00:02:36,884 --> 00:02:38,300
So there's the
vertical component.

59
00:02:38,300 --> 00:02:39,730
So let's solve for this.

60
00:02:39,730 --> 00:02:42,190
So if you add 29.54
to both sides,

61
00:02:42,190 --> 00:02:46,590
you get the vertical component
of your final velocity.

62
00:02:46,590 --> 00:02:48,230
Well, this is a
vertical component,

63
00:02:48,230 --> 00:02:50,390
I didn't mark it
up here properly--

64
00:02:50,390 --> 00:02:57,670
is equal to 29.54 meters
per second plus 9.8 plus --

65
00:02:57,670 --> 00:03:00,790
or I should say minus--
meters per second.

66
00:03:00,790 --> 00:03:08,120
Minus 9.8 meters per second
squared, times 5.67 seconds.

67
00:03:08,120 --> 00:03:10,550
The seconds cancel out
with one of these seconds.

68
00:03:10,550 --> 00:03:12,630
So everything is
meters per second.

69
00:03:12,630 --> 00:03:17,820
And so, get the
calculator out again,

70
00:03:17,820 --> 00:03:27,580
we have 29.54 minus
9.8 times 5.67.

71
00:03:27,580 --> 00:03:35,550
So we get our change-- our final
velocity is negative 26.03.

72
00:03:35,550 --> 00:03:40,564
So this is negative
26.03 meters per second.

73
00:03:40,564 --> 00:03:41,980
And you might say
wait, wait Sal ,

74
00:03:41,980 --> 00:03:45,290
what is this negative 26.03
meters per second mean?

75
00:03:45,290 --> 00:03:48,010
Remember, when we're dealing
in the vertical dimension,

76
00:03:48,010 --> 00:03:51,050
positive means up,
negative mean down.

77
00:03:51,050 --> 00:03:55,820
So it means we're going 26.03
meters per second downwards.

78
00:03:55,820 --> 00:04:00,860
Downwards, right when we land.

79
00:04:00,860 --> 00:04:04,880
So what is our
total velocity when

80
00:04:04,880 --> 00:04:07,190
we fall back to that landing?

81
00:04:07,190 --> 00:04:10,440
So the vertical
component of our velocity

82
00:04:10,440 --> 00:04:18,459
is negative 29.06 times .03
in the downward direction.

83
00:04:18,459 --> 00:04:21,450
And the horizontal component
of our velocity, we know,

84
00:04:21,450 --> 00:04:24,010
hadn't changed the entire time.

85
00:04:24,010 --> 00:04:28,410
That, we figured out, was
30 cosine of 80 degrees.

86
00:04:28,410 --> 00:04:31,720
So that over here, is
30 cosine of 80 degrees.

87
00:04:31,720 --> 00:04:33,760
I'll get the calculator
out to calculate it.

88
00:04:33,760 --> 00:04:40,290
30 cosine of 80 degrees,
which is equal to 5.21.

89
00:04:40,290 --> 00:04:44,080
So this is 5.21
meters per second.

90
00:04:44,080 --> 00:04:46,390
These are both in
meters per second.

91
00:04:46,390 --> 00:04:48,570
So what is the total velocity?

92
00:04:48,570 --> 00:04:50,530
Well, I can do
the head to tails.

93
00:04:50,530 --> 00:04:55,730
So I can shift this guy
over so that its tail is

94
00:04:55,730 --> 00:04:58,530
at the head of the blue vector.

95
00:04:58,530 --> 00:04:59,780
So it would look like that.

96
00:04:59,780 --> 00:05:01,500
The length of
this-- the magnitude

97
00:05:01,500 --> 00:05:06,397
of our vertical
component, is 29.03.

98
00:05:06,397 --> 00:05:08,480
And then we could just use
the Pythagorean theorem

99
00:05:08,480 --> 00:05:12,949
to figure out the magnitude of
the total velocity upon impact.

100
00:05:12,949 --> 00:05:14,490
So the length of
that-- we could just

101
00:05:14,490 --> 00:05:16,470
use the Pythagorean theorem.

102
00:05:16,470 --> 00:05:18,710
So the magnitude of our
total velocity, that's

103
00:05:18,710 --> 00:05:19,980
this length right over here.

104
00:05:19,980 --> 00:05:23,730


105
00:05:23,730 --> 00:05:25,550
The magnitude of
our total velocity,

106
00:05:25,550 --> 00:05:27,800
our total final velocity
I guess we can say,

107
00:05:27,800 --> 00:05:31,540
is going to be equal to-- well
that's-- let me write it this

108
00:05:31,540 --> 00:05:32,412
way.

109
00:05:32,412 --> 00:05:33,870
The magnitude of
our total velocity

110
00:05:33,870 --> 00:05:36,328
is going to be equal to square
root-- this is just straight

111
00:05:36,328 --> 00:05:40,640
from the Pythagorean
theorem-- of 5.21

112
00:05:40,640 --> 00:05:48,070
squared plus 29.03 squared.

113
00:05:48,070 --> 00:05:53,010
And we get it as
being the second--

114
00:05:53,010 --> 00:06:04,350
the square root of 5.21
squared plus 29.03 squared

115
00:06:04,350 --> 00:06:08,870
gives us 29.49
meters per second.

116
00:06:08,870 --> 00:06:12,180
This is equal to 29.49
meters per second.

117
00:06:12,180 --> 00:06:14,440
That is the magnitude
of our final velocity,

118
00:06:14,440 --> 00:06:17,120
but we also need to
figure out its direction.

119
00:06:17,120 --> 00:06:19,160
And so we need to
figure out this angle.

120
00:06:19,160 --> 00:06:22,320
And now we're talking about
an angle below the horizontal.

121
00:06:22,320 --> 00:06:24,734
Or, if you wanted to view
it in kind of pure terms,

122
00:06:24,734 --> 00:06:26,234
it would be a
negative angle-- or we

123
00:06:26,234 --> 00:06:28,560
could say an angle
below the horizontal.

124
00:06:28,560 --> 00:06:30,430
So what is this angle
right over here?

125
00:06:30,430 --> 00:06:32,160
So if we view it as
a positive angle just

126
00:06:32,160 --> 00:06:34,240
in the traditional
trigonometric way,

127
00:06:34,240 --> 00:06:37,602
we could say that the-- we could
use any of the trig functions,

128
00:06:37,602 --> 00:06:38,685
we could even use tangent.

129
00:06:38,685 --> 00:06:39,590
Let's use tangent.

130
00:06:39,590 --> 00:06:42,980
We could say that the
tangent of the angle, is

131
00:06:42,980 --> 00:06:45,410
equal to the opposite
over the adjacent--

132
00:06:45,410 --> 00:06:50,690
is equal to 29.03 over 5.21.

133
00:06:50,690 --> 00:06:54,140
Or that theta is equal
to the inverse tangent,

134
00:06:54,140 --> 00:07:02,340
or the arctangent
of 29.03 over 5.21.

135
00:07:02,340 --> 00:07:09,570
And that gives us-- we take
the inverse tangent of 29.03

136
00:07:09,570 --> 00:07:17,380
divided by 5.21, and
we get 79.8 degrees.

137
00:07:17,380 --> 00:07:21,740
But it's going to be
79.8 degrees south,

138
00:07:21,740 --> 00:07:23,285
or, I guess, below
the horizontal.

139
00:07:23,285 --> 00:07:26,040


140
00:07:26,040 --> 00:07:30,270
Or you could view this as an
angle of negative 79.8 degrees

141
00:07:30,270 --> 00:07:34,380
above the horizontal,
either one of those work.

142
00:07:34,380 --> 00:07:37,721
What's neat about this, is we
figured out our final velocity

143
00:07:37,721 --> 00:07:38,220
vector.

144
00:07:38,220 --> 00:07:40,990
The entire vector, we know
what that entire vector is.

145
00:07:40,990 --> 00:07:43,650


146
00:07:43,650 --> 00:07:49,790
It is 29.49 meters
per second at 79.8

147
00:07:49,790 --> 00:07:52,210
degrees below the horizontal.

148
00:07:52,210 --> 00:00:00,000