1 00:00:00,293 --> 00:00:01,699 - [Instructor] Let's talk about how to handle 2 00:00:01,699 --> 00:00:04,482 a horizontally launched projectile problem. 3 00:00:04,482 --> 00:00:06,581 These, technically speaking, if you already know 4 00:00:06,581 --> 00:00:09,358 how to do projectile problems, there is nothing new, 5 00:00:09,358 --> 00:00:11,683 except that there's one aspect of these problems 6 00:00:11,683 --> 00:00:14,196 that people get stumped by all of the time. 7 00:00:14,196 --> 00:00:15,778 So I'm gonna show you what that is in a minute 8 00:00:15,778 --> 00:00:18,184 so that you don't fall into the same trap. 9 00:00:18,184 --> 00:00:20,887 What we mean by a horizontally launched projectile 10 00:00:20,887 --> 00:00:23,011 is any object that gets launched 11 00:00:23,011 --> 00:00:26,404 in a completely horizontal velocity to start with. 12 00:00:26,404 --> 00:00:29,005 So if something is launched off of a cliff, let's say, 13 00:00:29,005 --> 00:00:30,921 in this straight horizontal direction 14 00:00:30,921 --> 00:00:33,768 with no vertical component to start with, 15 00:00:33,768 --> 00:00:35,940 then it's a horizontally launched projectile. 16 00:00:35,940 --> 00:00:37,291 What could that be? 17 00:00:37,291 --> 00:00:39,220 I mean a boring example, it's just a ball 18 00:00:39,220 --> 00:00:40,414 rolling off of a table. 19 00:00:40,414 --> 00:00:42,480 If you just roll the ball off of the table, 20 00:00:42,480 --> 00:00:45,320 then the velocity the ball has to start off with, 21 00:00:45,320 --> 00:00:47,541 if the table's flat and horizontal, 22 00:00:47,541 --> 00:00:50,530 the velocity of the ball initially would just be horizontal. 23 00:00:50,530 --> 00:00:54,015 So if the initial velocity of the object for a projectile 24 00:00:54,015 --> 00:00:57,124 is completely horizontal, then that object 25 00:00:57,124 --> 00:01:00,549 is a horizontally launched projectile. 26 00:01:00,549 --> 00:01:02,508 A more exciting example. 27 00:01:02,508 --> 00:01:03,997 People do crazy stuff. 28 00:01:03,997 --> 00:01:07,505 Let's say this person is gonna cliff dive or base jump, 29 00:01:07,505 --> 00:01:10,510 and they're gonna be like "whoa, let's do this." 30 00:01:10,510 --> 00:01:12,640 We're gonna do this, they're pumped up. 31 00:01:12,640 --> 00:01:15,053 They're gonna run but they don't jump off the cliff, 32 00:01:15,053 --> 00:01:17,177 they just run straight off of the cliff 33 00:01:17,177 --> 00:01:18,568 'cause they're kind of nervous. 34 00:01:18,568 --> 00:01:19,709 Let's say they run off of this cliff 35 00:01:19,709 --> 00:01:21,514 with five meters per second 36 00:01:21,514 --> 00:01:25,491 of initial velocity, straight off the cliff. 37 00:01:25,491 --> 00:01:27,456 And let's say they're completely crazy, 38 00:01:27,456 --> 00:01:30,933 let's say this cliff is 30 meters tall. 39 00:01:30,933 --> 00:01:33,759 So that's like over 90 feet. 40 00:01:33,759 --> 00:01:35,054 That is kind of crazy. 41 00:01:35,054 --> 00:01:38,662 So 30 meters tall, they launch, they fly through the air, 42 00:01:38,662 --> 00:01:41,983 there's water down here, so they initially went this way, 43 00:01:41,983 --> 00:01:43,750 and they start to fall down, 44 00:01:43,750 --> 00:01:45,504 and they do something like pschhh, 45 00:01:45,504 --> 00:01:46,966 and then they splash in the water, 46 00:01:46,966 --> 00:01:51,114 hopefully they don't hit any boats or fish down here. 47 00:01:51,114 --> 00:01:53,058 That fish already looks like he got hit. 48 00:01:53,058 --> 00:01:54,202 He or she. 49 00:01:54,202 --> 00:01:57,313 Alright, fish over here, person splashed into the water. 50 00:01:57,313 --> 00:02:00,148 We want to know, here's the question you might get asked: 51 00:02:00,148 --> 00:02:02,668 how far did this person go horizontally 52 00:02:02,668 --> 00:02:03,945 before striking the water? 53 00:02:03,945 --> 00:02:06,549 This is a classic problem, gets asked all the time. 54 00:02:06,549 --> 00:02:08,341 And if you were a cliff diver, 55 00:02:08,341 --> 00:02:09,995 I mean don't try this at home, 56 00:02:09,995 --> 00:02:11,728 but if you were a professional cliff diver 57 00:02:11,728 --> 00:02:15,187 you might want to know for this cliff high and this speed 58 00:02:15,187 --> 00:02:17,688 how fast do I have to run in order to avoid 59 00:02:17,688 --> 00:02:20,599 maybe the rocky shore right here 60 00:02:20,599 --> 00:02:22,376 that you might want to avoid. 61 00:02:22,376 --> 00:02:25,749 Maybe there's this nasty craggy cliff bottom here 62 00:02:25,749 --> 00:02:27,627 that you can't fall on. 63 00:02:27,627 --> 00:02:29,145 So how fast would I have to run 64 00:02:29,145 --> 00:02:31,355 in order to make it past that? 65 00:02:31,355 --> 00:02:34,462 Alright, so conceptually what's happening here, 66 00:02:34,462 --> 00:02:36,668 the same thing that happens for any projectile problem, 67 00:02:36,668 --> 00:02:39,452 the horizontal direction is happening 68 00:02:39,452 --> 00:02:41,527 independently of the vertical direction. 69 00:02:41,527 --> 00:02:43,861 And what I mean by that is that the horizontal velocity 70 00:02:43,861 --> 00:02:46,888 evolves independent to the vertical velocity. 71 00:02:46,888 --> 00:02:48,715 Let me get the velocity this color. 72 00:02:48,715 --> 00:02:50,956 So say the vertical velocity, 73 00:02:50,956 --> 00:02:52,759 or the vertical direction is pink, 74 00:02:52,759 --> 00:02:54,487 horizontal direction is green. 75 00:02:54,487 --> 00:02:56,896 This vertical velocity is gonna be changing 76 00:02:56,896 --> 00:02:59,485 but this horizontal velocity is just gonna remain the same. 77 00:02:59,485 --> 00:03:01,402 These do not influence each other. 78 00:03:01,402 --> 00:03:04,217 In other words, this horizontal velocity started at five, 79 00:03:04,217 --> 00:03:07,989 the person's always gonna have five meters per second 80 00:03:07,989 --> 00:03:09,327 of horizontal velocity. 81 00:03:09,327 --> 00:03:11,225 So this horizontal velocity is always gonna be 82 00:03:11,225 --> 00:03:12,841 five meters per second. 83 00:03:12,841 --> 00:03:15,339 The whole trip, assuming this person really is 84 00:03:15,339 --> 00:03:17,274 a freely flying projectile, 85 00:03:17,274 --> 00:03:19,554 assuming that there is no jet pack 86 00:03:19,554 --> 00:03:22,740 to propel them forward and no air resistance. 87 00:03:22,740 --> 00:03:25,226 This person's always gonna have five meters per second 88 00:03:25,226 --> 00:03:27,820 of horizontal velocity up onto the point 89 00:03:27,820 --> 00:03:29,810 right when they splash in the water, 90 00:03:29,810 --> 00:03:32,054 and then at that point there's forces from the water 91 00:03:32,054 --> 00:03:34,545 that influence this acceleration in various ways 92 00:03:34,545 --> 00:03:36,275 that we're not gonna consider. 93 00:03:36,275 --> 00:03:37,488 How about vertically? 94 00:03:37,488 --> 00:03:40,070 Vertically this person starts with no initial velocity. 95 00:03:40,070 --> 00:03:43,036 So this person just ran horizontally straight off the cliff 96 00:03:43,036 --> 00:03:45,249 and then they start to gain velocity. 97 00:03:45,249 --> 00:03:49,669 So they're gonna gain vertical velocity downward 98 00:03:49,669 --> 00:03:51,462 and maybe more vertical velocity 99 00:03:51,462 --> 00:03:53,280 because gravity keeps pulling, 100 00:03:53,280 --> 00:03:55,581 and then even more, this might go off the screen 101 00:03:55,581 --> 00:03:57,319 but it's gonna be really big. 102 00:03:57,319 --> 00:03:58,281 So a lot of vertical velocity, 103 00:03:58,281 --> 00:04:00,145 this should keep getting bigger and bigger and bigger 104 00:04:00,145 --> 00:04:03,049 because gravity's influencing this vertical direction 105 00:04:03,049 --> 00:04:05,426 but not the horizontal direction. 106 00:04:05,426 --> 00:04:07,476 So how do we solve this with math? 107 00:04:07,476 --> 00:04:08,977 Let's write down what we know. 108 00:04:08,977 --> 00:04:11,501 What we know is that horizontally this person started off 109 00:04:11,501 --> 00:04:13,748 with an initial velocity. 110 00:04:13,748 --> 00:04:16,442 V initial in the x, I could have written i for initial, 111 00:04:16,442 --> 00:04:18,611 but I wrote zero for v naught in the x, 112 00:04:18,611 --> 00:04:22,616 it still means initial velocity is five meters per second. 113 00:04:22,616 --> 00:04:24,319 And we don't know anything else in the x direction. 114 00:04:24,319 --> 00:04:26,740 You might think 30 meters is the displacement 115 00:04:26,740 --> 00:04:29,459 in the x direction, but that's a vertical distance. 116 00:04:29,459 --> 00:04:30,728 This is not telling us anything 117 00:04:30,728 --> 00:04:32,166 about this horizontal distance. 118 00:04:32,166 --> 00:04:34,184 This horizontal distance or displacement 119 00:04:34,184 --> 00:04:36,013 is what we want to know. 120 00:04:36,013 --> 00:04:38,014 This horizontal displacement in the x direction, 121 00:04:38,014 --> 00:04:39,447 that's what we want to solve for, 122 00:04:39,447 --> 00:04:42,321 so we're gonna declare our ignorance, write that here. 123 00:04:42,321 --> 00:04:43,481 We don't know how to find it 124 00:04:43,481 --> 00:04:45,515 but we want to know that we do want to find 125 00:04:45,515 --> 00:04:46,829 so I'm gonna write it there. 126 00:04:46,829 --> 00:04:48,696 How about in the y direction, what do we know? 127 00:04:48,696 --> 00:04:51,820 We know that the, alright, now we're gonna use this 30. 128 00:04:51,820 --> 00:04:54,635 You might want to say that delta y is positive 30 129 00:04:54,635 --> 00:04:57,089 but you would be wrong, and the reason is, 130 00:04:57,089 --> 00:04:59,588 this person fell downward 30 meters. 131 00:04:59,588 --> 00:05:00,421 Think about it. 132 00:05:00,421 --> 00:05:01,656 They started at the top of the cliff, 133 00:05:01,656 --> 00:05:03,920 ended at the bottom of the cliff. 134 00:05:03,920 --> 00:05:06,259 It means this person is going to end up 135 00:05:06,259 --> 00:05:07,656 below where they started, 136 00:05:07,656 --> 00:05:09,446 30 meters below where they started. 137 00:05:09,446 --> 00:05:12,754 So this has to be negative 30 meters for the displacement, 138 00:05:12,754 --> 00:05:14,655 assuming you're treating downward as negative 139 00:05:14,655 --> 00:05:17,028 which is typically the convention shows 140 00:05:17,028 --> 00:05:21,273 that downward is negative and leftward is negative. 141 00:05:21,273 --> 00:05:22,814 So if you choose downward as negative, 142 00:05:22,814 --> 00:05:24,984 this has to be a negative displacement. 143 00:05:24,984 --> 00:05:26,757 What else do we know vertically? 144 00:05:26,757 --> 00:05:30,362 Well, for a freely flying object we know 145 00:05:30,362 --> 00:05:32,268 that the acceleration vertically is always gonna be 146 00:05:32,268 --> 00:05:36,137 negative 9.8 meters per second squared, 147 00:05:36,137 --> 00:05:37,663 assuming downward is negative. 148 00:05:37,663 --> 00:05:39,954 Now, here's the point where people get stumped, 149 00:05:39,954 --> 00:05:41,934 and here's the part where people make a mistake. 150 00:05:41,934 --> 00:05:44,085 They want to say that the initial velocity 151 00:05:44,085 --> 00:05:46,820 in the y direction is five meters per second. 152 00:05:46,820 --> 00:05:48,497 I mean people are just dying to stick 153 00:05:48,497 --> 00:05:50,628 these five meters per second into here 154 00:05:50,628 --> 00:05:52,974 because that's the velocity that you were given. 155 00:05:52,974 --> 00:05:55,262 But this was a horizontal velocity. 156 00:05:55,262 --> 00:05:56,095 That's why this is called 157 00:05:56,095 --> 00:05:58,269 horizontally launched projectile motion, 158 00:05:58,269 --> 00:06:00,849 not vertically launched projectile motion. 159 00:06:00,849 --> 00:06:01,960 So think about it. 160 00:06:01,960 --> 00:06:04,099 The initial velocity in the vertical direction here 161 00:06:04,099 --> 00:06:07,004 was zero, there was no initial vertical velocity. 162 00:06:07,004 --> 00:06:09,631 This person was not launched vertically up 163 00:06:09,631 --> 00:06:10,924 or vertically down, 164 00:06:10,924 --> 00:06:13,491 this person was just launched straight horizontally, 165 00:06:13,491 --> 00:06:15,000 and so the initial velocity 166 00:06:15,000 --> 00:06:17,347 in the vertical direction is just zero. 167 00:06:17,347 --> 00:06:18,424 People don't like that. 168 00:06:18,424 --> 00:06:20,142 They're like "hold on a minute." 169 00:06:20,142 --> 00:06:22,751 They're like, this person is gonna start gaining, 170 00:06:22,751 --> 00:06:24,831 alright, this person is gonna start gaining velocity 171 00:06:24,831 --> 00:06:26,426 right when they leave the cliff, 172 00:06:26,426 --> 00:06:28,260 this starts getting bigger and bigger and bigger 173 00:06:28,260 --> 00:06:29,810 in the downward direction. 174 00:06:29,810 --> 00:06:32,001 But that's after you leave the cliff. 175 00:06:32,001 --> 00:06:34,363 We're talking about right as you leave the cliff. 176 00:06:34,363 --> 00:06:35,703 That moment you left the cliff 177 00:06:35,703 --> 00:06:38,019 there was only horizontal velocity, 178 00:06:38,019 --> 00:06:41,205 which means you started with no initial vertical velocity. 179 00:06:41,205 --> 00:06:43,423 So this is the part people get confused by 180 00:06:43,423 --> 00:06:46,347 because this is not given to you explicitly in the problem. 181 00:06:46,347 --> 00:06:49,342 The problem won't say, "Find the distance for a cliff diver 182 00:06:49,342 --> 00:06:52,911 "assuming the initial velocity in the y direction was zero." 183 00:06:52,911 --> 00:06:54,131 Now, they're just gonna say, 184 00:06:54,131 --> 00:06:56,547 "A cliff diver ran horizontally off of a cliff. 185 00:06:56,547 --> 00:06:57,659 "Find this stuff." 186 00:06:57,659 --> 00:06:59,535 And you're just gonna have to know that okay, 187 00:06:59,535 --> 00:07:01,511 if I run off of a cliff horizontally 188 00:07:01,511 --> 00:07:03,529 or something gets shot horizontally, 189 00:07:03,529 --> 00:07:06,169 that means there is no vertical velocity to start with, 190 00:07:06,169 --> 00:07:08,301 I'm gonna have to plug this initial velocity 191 00:07:08,301 --> 00:07:10,404 in the y direction as zero. 192 00:07:10,404 --> 00:07:11,635 So that's the trick. 193 00:07:11,635 --> 00:07:13,981 Don't fall for it now you know how to deal with it. 194 00:07:13,981 --> 00:07:16,663 So we want to solve for displacement in the x direction, 195 00:07:16,663 --> 00:07:18,868 but how many variables we know in the y direction? 196 00:07:18,868 --> 00:07:20,148 I mean we know all of this. 197 00:07:20,148 --> 00:07:20,981 This is good. 198 00:07:20,981 --> 00:07:22,871 But we can't use this to solve directly 199 00:07:22,871 --> 00:07:24,566 for the displacement in the x direction. 200 00:07:24,566 --> 00:07:27,361 We need to use this to solve for the time 201 00:07:27,361 --> 00:07:28,650 because the time is gonna be the same 202 00:07:28,650 --> 00:07:30,718 for the x direction and the y direction. 203 00:07:30,718 --> 00:07:33,091 So I find the time I can plug back in over to there, 204 00:07:33,091 --> 00:07:35,630 because think about it, the time it takes for this trip 205 00:07:35,630 --> 00:07:37,691 is gonna be the time it takes for this trip. 206 00:07:37,691 --> 00:07:39,599 It doesn't matter whether I call it the x direction 207 00:07:39,599 --> 00:07:43,115 or y direction, time is the same for both directions. 208 00:07:43,115 --> 00:07:45,431 In other words, the time it takes for this displacement 209 00:07:45,431 --> 00:07:47,739 of negative 30 is gonna be the time it takes 210 00:07:47,739 --> 00:07:50,227 for this displacement of whatever this is 211 00:07:50,227 --> 00:07:51,404 that we're gonna find. 212 00:07:51,404 --> 00:07:52,724 So let's solve for the time. 213 00:07:52,724 --> 00:07:53,983 Now, how will we do that? 214 00:07:53,983 --> 00:07:55,103 Think about it. 215 00:07:55,103 --> 00:07:57,439 We know the displacement, we know the acceleration, 216 00:07:57,439 --> 00:08:00,660 we know the initial velocity, and we know the time. 217 00:08:00,660 --> 00:08:02,499 But we don't know the final velocity 218 00:08:02,499 --> 00:08:05,059 and we're not asked to find the final velocity, 219 00:08:05,059 --> 00:08:06,307 we don't want to know it. 220 00:08:06,307 --> 00:08:08,545 So let's use a formula that doesn't involve 221 00:08:08,545 --> 00:08:11,470 the final velocity and that would look like this. 222 00:08:11,470 --> 00:08:13,720 So if we use delta y equals 223 00:08:15,220 --> 00:08:18,155 v initial in the y direction times time 224 00:08:18,155 --> 00:08:21,185 plus one half acceleration in the y direction 225 00:08:21,185 --> 00:08:23,141 times time squared. 226 00:08:23,141 --> 00:08:25,028 Alright, now we can plug in values. 227 00:08:25,028 --> 00:08:29,169 My displacement in the y direction is negative 30. 228 00:08:29,169 --> 00:08:32,245 My initial velocity in the y direction is zero. 229 00:08:32,245 --> 00:08:34,236 This is where it would happen, this is where the mistake 230 00:08:34,236 --> 00:08:36,675 would happen, people just really want 231 00:08:36,676 --> 00:08:38,219 to plug that five in over here. 232 00:08:38,219 --> 00:08:39,244 But don't do it, it's a trap. 233 00:08:39,244 --> 00:08:41,332 So, zero times t is just zero 234 00:08:41,332 --> 00:08:43,295 so that whole term is zero. 235 00:08:43,296 --> 00:08:45,393 Plus one half, the acceleration 236 00:08:45,393 --> 00:08:48,893 is negative 9.8 meters per second squared. 237 00:08:50,694 --> 00:08:53,615 And then times t squared, alright, now I can solve for t. 238 00:08:53,615 --> 00:08:54,919 I'm gonna solve for t, 239 00:08:54,919 --> 00:08:56,778 and then I'd have to take the square root of both sides 240 00:08:56,778 --> 00:08:59,122 because it's t squared, and what would I get? 241 00:08:59,122 --> 00:09:01,256 I'd have to multiply both sides by two. 242 00:09:01,256 --> 00:09:04,423 So I get negative 30 meters times two, 243 00:09:05,657 --> 00:09:07,129 and then I have to divide both sides 244 00:09:07,129 --> 00:09:11,296 by negative 9.8 meters per second squared, equals, 245 00:09:12,155 --> 00:09:14,988 notice if you would have forgotten 246 00:09:15,906 --> 00:09:17,716 this negative up here for negative 30, 247 00:09:17,716 --> 00:09:20,399 you come down here, this would be a positive up top. 248 00:09:20,399 --> 00:09:22,101 You'd have a negative on the bottom. 249 00:09:22,101 --> 00:09:23,606 You'd have to plug this in, you'd have to try to take 250 00:09:23,606 --> 00:09:25,312 the square root of a negative number. 251 00:09:25,312 --> 00:09:26,792 Your calculator would have been all like, 252 00:09:26,792 --> 00:09:28,166 "I don't know what that means," 253 00:09:28,166 --> 00:09:30,482 and you're gonna be like, "Er, am I stuck?" 254 00:09:30,482 --> 00:09:32,960 So you'd start coming back here probably and be like, 255 00:09:32,960 --> 00:09:36,271 "Let's just make stuff positive and see if that works." 256 00:09:36,271 --> 00:09:39,494 It would work because look at these negatives canceled 257 00:09:39,494 --> 00:09:41,160 but it's best to just know 258 00:09:41,160 --> 00:09:43,033 what you're talking about in the first place. 259 00:09:43,033 --> 00:09:44,948 So be careful: plug in your negatives 260 00:09:44,948 --> 00:09:46,692 and things will work out alright. 261 00:09:46,692 --> 00:09:47,821 So if you solve this you get 262 00:09:47,821 --> 00:09:50,762 that the time it took is 2.47 seconds. 263 00:09:50,762 --> 00:09:52,305 It's actually a long time. 264 00:09:52,305 --> 00:09:53,931 It might seem like you're falling for a long time 265 00:09:53,931 --> 00:09:55,809 sometimes when you're like jumping off of a table, 266 00:09:55,809 --> 00:09:57,446 jumping off of a trampoline, 267 00:09:57,446 --> 00:09:58,919 but it's usually like a fraction of a second. 268 00:09:58,919 --> 00:10:01,228 This is actually a long time, two and a half seconds 269 00:10:01,228 --> 00:10:02,620 of free fall's a long time. 270 00:10:02,620 --> 00:10:04,361 So we could take this, that's how long 271 00:10:04,361 --> 00:10:06,638 it took to displace by 30 meters vertically, 272 00:10:06,638 --> 00:10:08,584 but that's gonna be how long it took to displace 273 00:10:08,584 --> 00:10:10,267 this horizontal direction. 274 00:10:10,267 --> 00:10:11,676 We can use the same formula. 275 00:10:11,676 --> 00:10:15,773 We can say that well, if delta x equals 276 00:10:15,773 --> 00:10:17,473 v initial in the x direction, 277 00:10:17,473 --> 00:10:21,104 I'm just using the same formula but in the x direction, 278 00:10:21,104 --> 00:10:23,354 plus one half ax t squared. 279 00:10:24,189 --> 00:10:28,356 So the same formula as this just in the x direction. 280 00:10:29,324 --> 00:10:31,870 Delta x is just dx, we already gave that a name, 281 00:10:31,870 --> 00:10:34,054 so let's just call this dx. 282 00:10:34,054 --> 00:10:36,312 So I'm gonna scooch this equation over here. 283 00:10:36,312 --> 00:10:39,849 Dx is delta x, that equals the initial velocity 284 00:10:39,849 --> 00:10:41,808 in the x direction, that's five. 285 00:10:41,808 --> 00:10:43,246 Alright, this is really five. 286 00:10:43,246 --> 00:10:45,506 In the x direction the initial velocity 287 00:10:45,506 --> 00:10:49,122 really was five meters per second. 288 00:10:49,122 --> 00:10:50,382 How about the initial time? 289 00:10:50,382 --> 00:10:52,341 Oh sorry, the time, there is no initial time. 290 00:10:52,341 --> 00:10:55,206 The time here was 2.47 seconds. 291 00:10:55,206 --> 00:10:57,159 This was the time interval. 292 00:10:57,159 --> 00:10:59,417 The time between when the person jumped, 293 00:10:59,417 --> 00:11:00,746 or ran off the cliff, 294 00:11:00,746 --> 00:11:04,397 and when the person splashed in the water was 2.4, 295 00:11:04,397 --> 00:11:07,064 let me erase this, 2.47 seconds. 296 00:11:09,778 --> 00:11:13,278 So 2.47 seconds, and this comes over here. 297 00:11:14,488 --> 00:11:15,909 How about this ax? 298 00:11:15,909 --> 00:11:17,109 This ax is zero. 299 00:11:17,109 --> 00:11:18,977 Remember there's nothing compelling this person 300 00:11:18,977 --> 00:11:21,504 to start accelerating in x direction. 301 00:11:21,504 --> 00:11:24,282 If they've got no jet pack, there is no air resistance, 302 00:11:24,282 --> 00:11:25,296 there is no reason this person 303 00:11:25,296 --> 00:11:27,485 is gonna accelerate horizontally, 304 00:11:27,485 --> 00:11:30,265 they maintain the same velocity the whole way. 305 00:11:30,265 --> 00:11:31,098 So what do we get? 306 00:11:31,098 --> 00:11:34,012 If we solve this for dx, we'd get that dx 307 00:11:34,012 --> 00:11:36,095 is about 12.4, I believe. 308 00:11:37,712 --> 00:11:39,851 Let's see, I calculated this. 309 00:11:39,851 --> 00:11:41,184 12.4-ish meters. 310 00:11:42,739 --> 00:11:45,014 Okay, so if these rocks down here 311 00:11:45,014 --> 00:11:46,600 extend more than 12 meters, 312 00:11:46,600 --> 00:11:48,495 you definitely don't want to do this. 313 00:11:48,495 --> 00:11:49,436 I mean if it's even close 314 00:11:49,436 --> 00:11:51,356 you probably wouldn't want do this. 315 00:11:51,356 --> 00:11:54,847 In fact, just for safety don't try this at home, 316 00:11:54,847 --> 00:11:56,522 leave this to professional cliff divers. 317 00:11:56,522 --> 00:11:58,698 I'm just saying if you were one and you wanted to calculate 318 00:11:58,698 --> 00:12:02,228 how far you'd make it, this is how you would do it. 319 00:12:02,228 --> 00:12:05,450 So, long story short, the way you do this problem 320 00:12:05,450 --> 00:12:07,660 and the mistakes you would want to avoid are: 321 00:12:07,660 --> 00:12:09,467 make sure you're plugging your negative displacement 322 00:12:09,467 --> 00:12:11,355 because you fell downward, 323 00:12:11,355 --> 00:12:12,873 but the big one is make sure you know 324 00:12:12,873 --> 00:12:16,373 that the initial vertical velocity is zero 325 00:12:17,472 --> 00:12:20,165 because there is only horizontal velocity to start with. 326 00:12:20,165 --> 00:12:21,856 That's not gonna be given explicitly, 327 00:12:21,856 --> 00:12:24,167 you're just gonna have to provide that on your own 328 00:12:24,167 --> 00:00:00,000 and your own knowledge of physics.