WEBVTT 1 00:00:00.512 --> 00:00:02.816 Welcome to Brainfuse! 2 00:00:05.376 --> 00:00:11.520 We launched a marshmallow in part 1, and to show some progress in 3 00:00:11.776 --> 00:00:14.336 Part 2, we are going to 4 00:00:14.336 --> 00:00:20.464 Drop 2 marshmallows. So here's a problem that will let us do that. 5 00:00:20.464 --> 00:00:27.136 Two marshmallows are dropped out of a window 30 m above an alley where no one can be harmed by dropped desserts. 6 00:00:27.392 --> 00:00:33.330 One marshmallow is released with an initial velocity of 0 m/s, 7 00:00:33.536 --> 00:00:39.936 falling only by force of gravity. The other one is thrown straight down with an initial velocity of 8 00:00:40.192 --> 00:00:46.336 10 m/s. How many seconds earlier does the thrown object reach the ground? 9 00:00:46.592 --> 00:00:52.736 We can use the projectile motion formula to solve this problem. 10 00:00:53.760 --> 00:00:55.552 The final height 11 00:00:55.808 --> 00:00:57.600 Of the marshmallows 12 00:01:04.256 --> 00:01:07.072 That's equal to negative 1/2 13 00:01:07.584 --> 00:01:09.888 Of the acceleration of gravity 14 00:01:11.424 --> 00:01:15.264 times t-squared, 15 00:01:15.264 --> 00:01:15.264 16 00:01:16.032 --> 00:01:18.336 And we need to add to that 17 00:01:18.848 --> 00:01:20.640 the initial velocity 18 00:01:23.200 --> 00:01:25.248 Times time. 19 00:01:27.296 --> 00:01:29.344 Plus, what are we missing? 20 00:01:29.856 --> 00:01:31.392 The initial height, 21 00:01:34.720 --> 00:01:40.864 Since we are working with two objects in this problem, we can make a table to keep track of the data. 22 00:01:56.736 --> 00:02:02.880 I need three rows and five columns. 23 00:02:05.853 --> 00:02:10.048 Here is the row for the dropped marshmallow, 24 00:02:10.048 --> 00:02:10.048 25 00:02:12.096 --> 00:02:14.144 And a row for the thrown one. 26 00:02:29.504 --> 00:02:31.552 Let's just add the labels. 27 00:02:36.160 --> 00:02:38.464 We have our dropped 28 00:02:45.376 --> 00:02:47.168 and our thrown marshmallow. 29 00:02:57.920 --> 00:02:59.200 The initial height, 30 00:03:04.320 --> 00:03:05.856 The final height, 31 00:03:07.136 --> 00:03:09.184 Our initial velocity, 32 00:03:11.744 --> 00:03:13.280 And the time. 33 00:03:17.888 --> 00:03:19.936 And what information are we given? 34 00:03:21.472 --> 00:03:24.288 Two marshmallows are dropped out of a window 35 00:03:24.544 --> 00:03:27.616 30 meters above an alley. 36 00:03:27.616 --> 00:03:27.616 37 00:03:27.872 --> 00:03:31.456 So our initial height or altitude of the marshmallows 38 00:03:38.624 --> 00:03:42.464 Okay, what else do we know? We know that one marshmallow 39 00:03:42.720 --> 00:03:46.048 Is released with an initial velocity of 0 40 00:03:46.560 --> 00:03:47.840 and that should be meters, 41 00:03:51.168 --> 00:03:53.472 Meters per second, 42 00:03:55.520 --> 00:03:57.568 That would be the dropped marshmallow, 43 00:04:04.224 --> 00:04:07.296 Falling only by force of gravity. The other one 44 00:04:07.296 --> 00:04:11.136 Is thrown straight down with an initial velocity of 45 00:04:11.392 --> 00:04:12.928 10 m/s. 46 00:04:16.000 --> 00:04:19.779 So how many seconds earlier does the thrown object reach the ground? 47 00:04:19.779 --> 00:04:23.424 In this problem we are comparing their times, 48 00:04:24.704 --> 00:04:27.520 Their travel times as they fell from the window. 49 00:04:28.544 --> 00:04:30.592 We'll call the dropped marshmallow's time 50 00:04:31.104 --> 00:04:34.944 t sub d, and the thrown marshmallows time 51 00:04:35.200 --> 00:04:36.992 t sub x, 52 00:04:36.992 --> 00:04:39.296 Because t sub t would just be confusing. 53 00:04:39.552 --> 00:04:43.392 All right, in the last lesson we 54 00:04:44.160 --> 00:04:51.945 Found that the acceleration of gravity in meters would be -9.8 meters per second squared, 55 00:04:51.945 --> 00:04:51.945 56 00:04:51.945 --> 00:04:58.752 So half of that value is -4.9 m/s^2, and 57 00:04:59.008 --> 00:05:02.080 Scrolling down to give us some room to work. 58 00:05:03.872 --> 00:05:10.016 The final value in this table is the final height. So we can figure that out 59 00:05:10.272 --> 00:05:15.904 Because we are finding out how many seconds it took for the marshmallow to reach the ground 60 00:05:16.672 --> 00:05:18.976 And in this case the ground is equal to 61 00:05:19.488 --> 00:05:20.768 0 meters 62 00:05:23.072 --> 00:05:26.400 Let's now solve for the time of the dropped marshmallow. 63 00:05:27.680 --> 00:05:29.984 That would be the initial height, 64 00:05:30.240 --> 00:05:31.520 0 meters, 65 00:05:31.520 --> 00:05:37.152 Is equal to -4.9 m/s^2 66 00:05:37.152 --> 00:05:37.152 67 00:05:37.920 --> 00:05:40.480 Times t squared, plus 68 00:05:42.016 --> 00:05:44.576 0 m/s times t, 69 00:05:44.832 --> 00:05:46.624 This is zero we can leave it out, 70 00:05:47.392 --> 00:05:48.160 Plus 71 00:05:49.184 --> 00:05:52.000 The initial height which is 30 meters. 72 00:05:54.530 --> 00:06:00.448 Again, this is a quadratic equation so we can use the quadratic formula to solve for t. 73 00:06:01.984 --> 00:06:06.848 Here's a glimpse of that formula again as a quick reference. 74 00:06:08.711 --> 00:06:22.495 In this case, a would be equal to -4.9, b would be equal to the initial velocity or 0, and c would be equal to 30. 75 00:06:22.495 --> 00:06:28.608 So we plug those into the quadratic formula. The quadratic formula shows us that 76 00:06:28.864 --> 00:06:35.669 t sub d is equal to two possible values, it would be positive or negative 77 00:06:35.669 --> 00:06:42.236 2.47 seconds, and since this marshmallow did not time travel, 78 00:06:42.236 --> 00:06:49.539 The best choice is positive 2.47 seconds. 79 00:06:50.877 --> 00:06:54.208 So let's compare this time to the 80 00:06:54.208 --> 00:07:00.608 Thrown marshmallow's time. 81 00:07:04.372 --> 00:07:07.008 All right, so switching to 82 00:07:07.008 --> 00:07:13.408 The thrown marshmallow, we have zero meters as the final height again, 83 00:07:13.664 --> 00:07:20.886 -4.9 m/s^2, the acceleration of gravity stays the same, 84 00:07:20.886 --> 00:07:26.464 Times t-squared, plus our initial 85 00:07:26.464 --> 00:07:32.608 Velocity, 10 m/s, and that is 86 00:07:32.864 --> 00:07:39.008 Multiplied by our time, and finally our initial height which is 87 00:07:39.008 --> 00:07:45.408 30 meters. Okay, again this is a 88 00:07:45.664 --> 00:07:52.778 Quadratic equation so we use the quadratic formula if it cannot be easily factored. 89 00:07:55.304 --> 00:07:57.912 Took the tail off that Q there. 90 00:07:57.912 --> 00:08:05.548 The quadratic formula: In this case, a would be equal to -4.9, 91 00:08:05.548 --> 00:08:11.008 b is equal to 10, that's a big change in this equation, 92 00:08:11.264 --> 00:08:17.408 And C is equal to 30. When we plug those values into the quadratic formula, 93 00:08:17.664 --> 00:08:23.808 We find that t sub x, the time of our thrown marshmallow, equals 94 00:08:23.808 --> 00:08:31.542 Either -3.7 seconds or +1.66. 95 00:08:31.542 --> 00:08:36.607 So which one makes the most sense? The positive number 96 00:08:36.864 --> 00:08:43.878 Makes the most sense here. So now we have the values we need to solve this problem. 97 00:08:43.879 --> 00:08:49.663 All right, so what are we need to figure out? Scroll back up to see. How many seconds earlier 98 00:08:49.664 --> 00:08:55.808 Does the thrown object reach the ground? Let's find the difference between their times. 99 00:08:56.064 --> 00:09:02.208 Hope I'm not making you seasick. We have the time of the dropped object 100 00:09:02.464 --> 00:09:08.608 Minus the time of our thrown object, 101 00:09:08.864 --> 00:09:15.008 And that is equal to 2.47 seconds 102 00:09:15.264 --> 00:09:21.408 Minus 1.66 seconds 103 00:09:21.664 --> 00:09:27.808 And the difference is, ready, 0.81 seconds. 104 00:09:34.464 --> 00:09:40.608 So the marshmallow that was angrily thrown straight down from the window 105 00:09:40.864 --> 00:09:47.008 Landed 81 hundredths of a second earlier than our dropped marshmallow. 106 00:09:47.264 --> 00:09:55.001 For more practice with dropping objects you can log on to Live Help to work on problems like this with the Brainfuse tutors. 107 00:09:55.001 --> 00:09:58.272 And thanks so much for watching this lesson.