1 00:00:00,767 --> 00:00:02,045 - [Voiceover] So I've got a rocket here. 2 00:00:02,045 --> 00:00:05,377 And this rocket is going to launch a projectile, 3 00:00:05,377 --> 00:00:07,424 maybe it's a rock of some kind, 4 00:00:07,424 --> 00:00:10,641 with the velocity of ten meters per second. 5 00:00:10,641 --> 00:00:13,340 And the direction of that velocity 6 00:00:13,340 --> 00:00:15,239 is going to be be 30 degrees, 7 00:00:15,239 --> 00:00:17,856 30 degrees upwards from the horizontal. 8 00:00:17,856 --> 00:00:20,347 Or the angle between the direction of the launch 9 00:00:20,347 --> 00:00:22,777 and horizontal is 30 degrees. 10 00:00:22,777 --> 00:00:24,221 And what we want to figure out in this video 11 00:00:24,221 --> 00:00:26,798 is how far does the rock travel? 12 00:00:26,798 --> 00:00:29,678 We want to figure out how, 13 00:00:29,678 --> 00:00:31,595 how far does it travel? 14 00:00:32,859 --> 00:00:34,109 Does it travel? 15 00:00:35,819 --> 00:00:37,529 And to simplify this problem, 16 00:00:37,529 --> 00:00:38,362 what we're gonna do is 17 00:00:38,362 --> 00:00:40,484 we're gonna break down this velocity vector 18 00:00:40,484 --> 00:00:43,309 into its vertical and horizontal components. 19 00:00:43,309 --> 00:00:44,888 We're going to use a vertical component, 20 00:00:44,888 --> 00:00:46,513 so let me just draw it visually. 21 00:00:46,513 --> 00:00:47,976 So this velocity vector can be 22 00:00:47,976 --> 00:00:50,458 broken down into its vertical 23 00:00:50,458 --> 00:00:52,958 and its horizontal components. 24 00:00:53,953 --> 00:00:56,120 And its horizontal components. 25 00:00:56,120 --> 00:00:58,233 So we're gonna get some vertical component, 26 00:00:58,233 --> 00:01:01,356 some amount of velocity in the upwards direction, 27 00:01:01,356 --> 00:01:02,261 and we can figure, 28 00:01:02,261 --> 00:01:04,223 we can use that to figure out 29 00:01:04,223 --> 00:01:06,813 how long will this rock stay in the air. 30 00:01:06,813 --> 00:01:07,776 Because it doesn't matter 31 00:01:07,776 --> 00:01:09,580 what its horizontal component is. 32 00:01:09,580 --> 00:01:11,855 Its vertical component is gonna determine 33 00:01:11,855 --> 00:01:14,142 how quickly it decelerates due to gravity 34 00:01:14,142 --> 00:01:15,884 and then re-accelerated, and essentially 35 00:01:15,884 --> 00:01:18,049 how long it's going to be the air. 36 00:01:18,049 --> 00:01:20,626 And once we figure out how long it's in the air, 37 00:01:20,626 --> 00:01:22,971 we can multiply it by, 38 00:01:22,971 --> 00:01:24,320 we can multiply it by the 39 00:01:24,320 --> 00:01:26,923 horizontal component of the velocity, 40 00:01:26,923 --> 00:01:29,338 and that will tell us how far it travels. 41 00:01:29,338 --> 00:01:30,883 And, once again, the assumption 42 00:01:30,883 --> 00:01:31,962 that were making this videos 43 00:01:31,962 --> 00:01:34,679 is that air resistance is negligible. 44 00:01:34,679 --> 00:01:37,837 Obviously, if there was significant air resistance, 45 00:01:37,837 --> 00:01:40,634 this horizontal velocity would not stay constant 46 00:01:40,634 --> 00:01:42,144 while it's traveling through the air. 47 00:01:42,144 --> 00:01:43,452 But we're going to assume that it does, 48 00:01:43,452 --> 00:01:44,925 that this does not change, 49 00:01:44,925 --> 00:01:45,758 that it is negligible. 50 00:01:45,758 --> 00:01:47,562 We can assume that were doing this experiment 51 00:01:47,562 --> 00:01:49,278 on the moon if we wanted to have a, 52 00:01:49,278 --> 00:01:51,245 if we wanted to view it in purer terms. 53 00:01:51,245 --> 00:01:53,114 But let's solve the problem. 54 00:01:53,114 --> 00:01:54,113 So the first that we want to do 55 00:01:54,113 --> 00:01:57,247 is we wanna break down this velocity vector. 56 00:01:57,247 --> 00:01:59,105 We want to break down this velocity vector 57 00:01:59,105 --> 00:02:02,031 that has a magnitude of ten meters per second. 58 00:02:02,031 --> 00:02:05,815 And has an angle of 30 degrees with the horizontal. 59 00:02:05,815 --> 00:02:08,149 We want to break it down it with x- and y-components, 60 00:02:08,149 --> 00:02:10,750 or its horizontal and vertical components. 61 00:02:10,750 --> 00:02:13,307 so that's its horizontal, 62 00:02:13,307 --> 00:02:14,742 let me draw a little bit better, 63 00:02:14,742 --> 00:02:16,808 that's its horizontal component, 64 00:02:16,808 --> 00:02:19,502 and that its vertical component looks like this. 65 00:02:19,502 --> 00:02:21,662 This is its vertical component. 66 00:02:21,662 --> 00:02:24,074 So let's do the vertical component first. 67 00:02:24,074 --> 00:02:26,082 So how do we figure out the vertical component 68 00:02:26,082 --> 00:02:29,483 given that we know the hypotenuse of this right triangle 69 00:02:29,483 --> 00:02:31,469 and we know this angle right over here. 70 00:02:31,469 --> 00:02:34,325 And the angle, and the side, this vertical component, 71 00:02:34,325 --> 00:02:36,147 or the length of that vertical component, 72 00:02:36,147 --> 00:02:37,703 or the magnitude of it, 73 00:02:37,703 --> 00:02:40,245 is opposite the angle. 74 00:02:40,245 --> 00:02:41,743 So we want to figure out the opposite. 75 00:02:41,743 --> 00:02:44,471 We have to hypotenuse, so once again 76 00:02:44,471 --> 00:02:46,221 we write down so-cah, 77 00:02:47,530 --> 00:02:49,191 so-ca-toh-ah. 78 00:02:49,191 --> 00:02:52,338 Sin is opposite over hypotenuse. 79 00:02:52,338 --> 00:02:54,521 So we know that the sin, 80 00:02:54,521 --> 00:02:56,354 the sin of 30 degrees, 81 00:02:57,424 --> 00:02:59,513 the sin of 30 degrees, 82 00:02:59,513 --> 00:03:02,045 is going to be equal to the magnitude 83 00:03:02,045 --> 00:03:04,181 of our vertical component. 84 00:03:04,181 --> 00:03:07,750 So this is the magnitude of velocity, 85 00:03:07,750 --> 00:03:10,193 I'll say the velocity in the y direction. 86 00:03:10,193 --> 00:03:11,480 That's the vertical direction, 87 00:03:11,480 --> 00:03:13,546 y is the upwards direction. 88 00:03:13,546 --> 00:03:17,505 Is equal to the magnitude of our velocity 89 00:03:17,505 --> 00:03:20,710 of the velocity in the y direction. 90 00:03:20,710 --> 00:03:24,984 Divided by the magnitude of the hypotenuse, 91 00:03:24,984 --> 00:03:26,935 or the magnitude of our original vector. 92 00:03:26,935 --> 00:03:29,970 Divided by ten meters per second. 93 00:03:29,970 --> 00:03:31,803 Ten meters per second. 94 00:03:32,931 --> 00:03:34,710 And then, to solve for this quantity 95 00:03:34,710 --> 00:03:35,924 right over here, 96 00:03:35,924 --> 00:03:38,165 we multiply both sides by 10. 97 00:03:38,165 --> 00:03:41,076 And you get 10, sin of 30. 98 00:03:41,076 --> 00:03:42,909 10, sin of 30 degrees. 99 00:03:44,840 --> 00:03:47,314 10 sin of 30 degrees is going to be 100 00:03:47,314 --> 00:03:50,221 equal to the magnitude of our, 101 00:03:50,221 --> 00:03:53,425 the magnitude of our vertical component. 102 00:03:53,425 --> 00:03:56,397 And so what is the sin of 30 degrees? 103 00:03:56,397 --> 00:03:58,344 And this, you might have memorized this 104 00:03:58,344 --> 00:04:00,096 from your basic trigonometry class. 105 00:04:00,096 --> 00:04:01,993 You can get the calculator out if you want, 106 00:04:01,993 --> 00:04:04,037 but sin of 30 degrees is pretty straightforward. 107 00:04:04,037 --> 00:04:06,858 It is 1/2. So sin of 30 degrees, 108 00:04:06,858 --> 00:04:09,262 use a calculator if you don't remember that, or 109 00:04:09,262 --> 00:04:10,214 you remember it now so 110 00:04:10,214 --> 00:04:12,261 sin of 30 degrees is 1/2. 111 00:04:12,261 --> 00:04:14,186 And so 10 times 1/2 112 00:04:14,186 --> 00:04:16,507 is going to be five. 113 00:04:16,507 --> 00:04:17,784 So, and I forgot the units there, 114 00:04:17,785 --> 00:04:19,728 so it's five meters per second. 115 00:04:19,728 --> 00:04:21,892 Is equal to the magnitude, 116 00:04:21,892 --> 00:04:25,876 is equal to the magnitude of our vertical component. 117 00:04:25,876 --> 00:04:27,396 Let me get that in the right color. 118 00:04:27,396 --> 00:04:31,417 It's equal to the magnitude of our vertical component. 119 00:04:31,417 --> 00:04:32,392 So what does that do? 120 00:04:32,392 --> 00:04:33,225 What we're, 121 00:04:33,225 --> 00:04:35,973 this projectile, because vertical component 122 00:04:35,973 --> 00:04:37,529 is five meters per second, 123 00:04:37,529 --> 00:04:40,153 it will stay in the air the same amount of time 124 00:04:40,153 --> 00:04:42,351 as anything that has a vertical 125 00:04:42,351 --> 00:04:44,014 component of five meters per second. 126 00:04:44,014 --> 00:04:47,459 If you threw a rock or projectile straight up 127 00:04:47,459 --> 00:04:50,397 at a velocity five meters per second, 128 00:04:50,397 --> 00:04:52,124 that rocket projectile will stay 129 00:04:52,124 --> 00:04:54,462 up in the air as long as this one here 130 00:04:54,462 --> 00:04:56,946 because they have the same vertical component. 131 00:04:56,946 --> 00:05:00,070 So let's think about how long it will stay in the air. 132 00:05:00,070 --> 00:05:01,567 Since were dealing with a situation 133 00:05:01,567 --> 00:05:03,448 where we're starting in the ground 134 00:05:03,448 --> 00:05:04,946 and we're also finishing 135 00:05:04,946 --> 00:05:06,652 at the same elevation, 136 00:05:06,652 --> 00:05:09,067 and were assuming the air resistance is negligible, 137 00:05:09,067 --> 00:05:10,983 we can do a little bit of a simplification here. 138 00:05:10,983 --> 00:05:12,144 Although I'll do another version where 139 00:05:12,144 --> 00:05:13,440 we're doing the more complicated, 140 00:05:13,440 --> 00:05:17,137 but I guess the way that applies to more situations. 141 00:05:17,137 --> 00:05:18,220 We could say, 142 00:05:18,220 --> 00:05:19,394 we could say "well what is our 143 00:05:19,394 --> 00:05:21,469 "change in velocity here?" 144 00:05:21,469 --> 00:05:23,431 So if we think about just the vertical velocity, 145 00:05:23,431 --> 00:05:25,114 our initial velocity, 146 00:05:25,114 --> 00:05:26,368 let me write it this way. 147 00:05:26,368 --> 00:05:29,050 Our initial velocity, and we're talking, 148 00:05:29,050 --> 00:05:30,471 let me label all of this. 149 00:05:30,471 --> 00:05:32,062 So we're talking only in the vertical. 150 00:05:32,062 --> 00:05:33,385 Let me do all the vertical stuff 151 00:05:33,385 --> 00:05:34,660 that we wrote in blue. 152 00:05:34,660 --> 00:05:37,655 So vertical, were dealing with the vertical here. 153 00:05:37,655 --> 00:05:40,755 So our initial velocity, in the vertical direction, 154 00:05:40,755 --> 00:05:42,833 our initial velocity in the vertical direction 155 00:05:42,833 --> 00:05:45,655 is going to be five meters per second. 156 00:05:45,655 --> 00:05:47,803 Is going to be five meters per second. 157 00:05:47,803 --> 00:05:50,625 And we're going to use a convention, that up, 158 00:05:50,625 --> 00:05:55,259 that up is positive and that down is negative. 159 00:05:55,259 --> 00:05:57,697 And now what is going to be our final velocity? 160 00:05:57,697 --> 00:05:59,055 We're going to be going up 161 00:05:59,055 --> 00:06:01,017 and would be decelerated by gravity, 162 00:06:01,017 --> 00:06:02,887 We're gonna be stationary at some point. 163 00:06:02,887 --> 00:06:05,661 And then were to start accelerating back down. 164 00:06:05,661 --> 00:06:08,599 And, if we assume that air resistance is negligible, 165 00:06:08,599 --> 00:06:11,478 when we get back to ground level, 166 00:06:11,478 --> 00:06:13,776 we will have the same magnitude of velocity 167 00:06:13,776 --> 00:06:15,983 but will be going in the opposite direction. 168 00:06:15,983 --> 00:06:17,237 So our final velocity, remember, 169 00:06:17,237 --> 00:06:18,096 we're just talking about the 170 00:06:18,096 --> 00:06:19,911 vertical component right now. 171 00:06:19,911 --> 00:06:21,461 We haven't even thought about the horizontal. 172 00:06:21,461 --> 00:06:22,585 We're just trying to figure out 173 00:06:22,585 --> 00:06:25,603 how long does this thing stay in the air? 174 00:06:25,603 --> 00:06:29,121 So its final velocity is going to be negative five. 175 00:06:29,121 --> 00:06:30,886 Negative five 176 00:06:30,886 --> 00:06:32,069 meters per second. 177 00:06:32,069 --> 00:06:33,219 And this is initial velocity, 178 00:06:33,219 --> 00:06:35,704 the final velocity is going to be looking like that. 179 00:06:35,704 --> 00:06:38,305 Same magnitude, just in the opposite direction. 180 00:06:38,305 --> 00:06:39,825 So what's our change in velocity 181 00:06:39,825 --> 00:06:41,381 in the vertical direction? 182 00:06:41,381 --> 00:06:45,189 Change in velocity, in the vertical direction, 183 00:06:45,189 --> 00:06:47,397 or in the y-direction, is going to be 184 00:06:47,397 --> 00:06:51,994 our final velocity, negative five meters per second, 185 00:06:51,994 --> 00:06:53,550 minus our initial velocity, 186 00:06:53,550 --> 00:06:55,895 minus five meters per second, 187 00:06:55,895 --> 00:06:58,710 which is equal to negative 10 188 00:06:58,710 --> 00:07:00,646 meters per second. 189 00:07:00,646 --> 00:07:02,692 So how do we use this information 190 00:07:02,692 --> 00:07:05,051 to figure out how long it's in the air? 191 00:07:05,051 --> 00:07:06,340 Well we know! 192 00:07:06,340 --> 00:07:10,055 We know that our vertical, our change 193 00:07:10,055 --> 00:07:13,840 our change in our, in our vertical velocity, 194 00:07:13,840 --> 00:07:15,918 is going to be the same thing 195 00:07:15,918 --> 00:07:17,518 or it's equal to 196 00:07:17,518 --> 00:07:19,135 our acceleration 197 00:07:19,135 --> 00:07:20,842 in the vertical direction 198 00:07:20,842 --> 00:07:22,911 times the change in time. 199 00:07:22,911 --> 00:07:25,767 Times the amount of time that passes by. 200 00:07:25,767 --> 00:07:28,663 What's our acceleration in the vertical direction? 201 00:07:28,663 --> 00:07:30,602 What's the acceleration due to gravity, 202 00:07:30,602 --> 00:07:32,204 or acceleration that gravity, 203 00:07:32,204 --> 00:07:35,446 that the force of gravity has an object in freefall? 204 00:07:35,446 --> 00:07:37,281 and so this, right here, is going to be 205 00:07:37,281 --> 00:07:41,321 negative 9.8 meters per second squared. 206 00:07:41,321 --> 00:07:42,609 So this quantity over here is 207 00:07:42,609 --> 00:07:44,084 negative 10 meters per second, 208 00:07:44,084 --> 00:07:45,048 we figured that out, 209 00:07:45,048 --> 00:07:47,079 that's gonna be the change in velocity. 210 00:07:47,079 --> 00:07:49,889 Negative 10 meters per second 211 00:07:49,889 --> 00:07:51,607 is going to be equal to 212 00:07:51,607 --> 00:07:53,267 negative 9.8, 213 00:07:53,267 --> 00:07:56,286 negative 9.8 meters per second squared 214 00:07:56,286 --> 00:07:58,922 times our change in time. 215 00:07:58,922 --> 00:08:00,584 So to figure out the total amount of time 216 00:08:00,584 --> 00:08:01,479 that we are the air, 217 00:08:01,479 --> 00:08:03,701 we just divide both sides by 218 00:08:03,701 --> 00:08:06,932 negative 9.8 meters per second squared. 219 00:08:06,932 --> 00:08:08,219 So we get, 220 00:08:08,219 --> 00:08:09,052 lets just do that, 221 00:08:09,052 --> 00:08:11,297 I wanna do that in the same color. 222 00:08:11,297 --> 00:08:12,850 So I do it in, 223 00:08:12,850 --> 00:08:14,174 that's not, well, that close enough. 224 00:08:14,174 --> 00:08:16,269 So we get negative 9.8 225 00:08:16,269 --> 00:08:18,731 meters per second squared. 226 00:08:18,731 --> 00:08:22,085 Negative 9.8 meters per second squared. 227 00:08:22,085 --> 00:08:23,247 That cancels out, 228 00:08:23,247 --> 00:08:25,325 and I get my change in time. 229 00:08:25,325 --> 00:08:26,625 And I'll just get the calculator. 230 00:08:26,625 --> 00:08:28,123 I have a negative divided by a negative 231 00:08:28,123 --> 00:08:29,365 so that's a positive, which is good, 232 00:08:29,365 --> 00:08:31,246 because we want to go in positive time. 233 00:08:31,246 --> 00:08:32,929 We assume that the elapsed time 234 00:08:32,929 --> 00:08:34,461 is a positive one. 235 00:08:34,462 --> 00:08:35,419 And so what we get? 236 00:08:35,419 --> 00:08:37,932 If I get my calculator out, 237 00:08:37,933 --> 00:08:39,471 I get my calculator out. 238 00:08:39,471 --> 00:08:41,342 I have, this is the same thing as 239 00:08:41,342 --> 00:08:43,789 positive 10 divided by 9.8. 240 00:08:43,789 --> 00:08:45,372 10, divided by 9.8. 241 00:08:47,148 --> 00:08:48,315 Gives me 1.02. 242 00:08:49,923 --> 00:08:51,756 I'll just round to two digits 243 00:08:51,756 --> 00:08:53,289 right over there. 244 00:08:53,289 --> 00:08:55,706 So that gives me 1.02 seconds 245 00:08:58,119 --> 00:08:59,767 So our change in time, 246 00:08:59,767 --> 00:09:03,012 so this right over here is 1.02. 247 00:09:03,012 --> 00:09:05,538 So our change in time, 248 00:09:05,538 --> 00:09:09,033 delta t, I'm using lowercase now but 249 00:09:09,033 --> 00:09:10,810 I can make this all lower case. 250 00:09:10,810 --> 00:09:12,143 Is equal to 1.02 251 00:09:13,617 --> 00:09:14,700 1.02 seconds. 252 00:09:16,571 --> 00:09:18,297 Now how do we use this information 253 00:09:18,297 --> 00:09:21,990 to figure out how far this thing travels? 254 00:09:21,990 --> 00:09:23,802 Well if we assume that it retains 255 00:09:23,802 --> 00:09:27,064 its horizontal component of its velocity the whole time, 256 00:09:27,064 --> 00:09:29,189 we just assume we can this multiply that 257 00:09:29,189 --> 00:09:30,825 times our change in time 258 00:09:30,825 --> 00:09:32,799 and we'll get the total displacement 259 00:09:32,799 --> 00:09:35,665 in the horizontal direction. 260 00:09:35,665 --> 00:09:36,826 So to do that, we need to figure out 261 00:09:36,826 --> 00:09:38,104 this horizontal component, 262 00:09:38,104 --> 00:09:38,937 which we didn't do yet. 263 00:09:38,937 --> 00:09:41,933 So this is the component of our velocity 264 00:09:41,933 --> 00:09:44,646 in the x direction, or the horizontal direction. 265 00:09:44,646 --> 00:09:48,181 Once again, we break out a little bit of trigonometry. 266 00:09:48,181 --> 00:09:51,037 This side is adjacent to the angle, 267 00:09:51,037 --> 00:09:54,049 so the adjacent over hypotenuse is the cosine of the angle. 268 00:09:54,049 --> 00:09:57,009 Cosine of an angle is adjacent over hypotenuse. 269 00:09:57,009 --> 00:09:58,426 So we get cosine. 270 00:10:00,132 --> 00:10:02,594 Cosine of 30 degrees, 271 00:10:02,594 --> 00:10:04,114 I just want to make sure I color-code it right, 272 00:10:04,114 --> 00:10:07,215 cosine of 30 degrees is equal to 273 00:10:07,215 --> 00:10:08,982 the adjacent side. 274 00:10:08,982 --> 00:10:10,723 Is equal to the adjacent side, 275 00:10:10,723 --> 00:10:14,362 which is the magnitude of our horizontal component, 276 00:10:14,362 --> 00:10:17,722 is equal to the adjacent side over the hypotenuse. 277 00:10:17,722 --> 00:10:19,889 Over 10 meters per second. 278 00:10:21,194 --> 00:10:23,817 multiply both sides by 10 meters per second, 279 00:10:23,817 --> 00:10:27,776 you get the magnitude of our adjacent side, 280 00:10:27,776 --> 00:10:29,553 color transitioning is difficult, 281 00:10:29,553 --> 00:10:32,617 the magnitude of our adjacent side 282 00:10:32,617 --> 00:10:35,079 is equal to 10 meters per second. 283 00:10:35,079 --> 00:10:37,206 Is equal to 10 meters per second. 284 00:10:37,206 --> 00:10:38,751 Times the cosine, 285 00:10:38,751 --> 00:10:41,334 times the cosine of 30 degrees. 286 00:10:42,711 --> 00:10:44,187 And you might not remember 287 00:10:44,187 --> 00:10:45,568 the cosine of 30 degrees, 288 00:10:45,568 --> 00:10:47,252 you can use a calculator for this. 289 00:10:47,252 --> 00:10:49,063 Or you can just, if you do remember it, 290 00:10:49,063 --> 00:10:50,428 you know that it's the square root 291 00:10:50,428 --> 00:10:52,530 of three over two. 292 00:10:52,530 --> 00:10:54,921 Square root of three over two. 293 00:10:54,921 --> 00:10:56,848 So to figure out the actual component, 294 00:10:56,848 --> 00:10:58,787 I'll stop to get a calculator out if I want, 295 00:10:58,787 --> 00:10:59,732 well I don't have to use it, 296 00:10:59,732 --> 00:11:00,885 do it just yet, 297 00:11:00,885 --> 00:11:01,974 because I have 10 times 298 00:11:01,974 --> 00:11:03,797 the square root of three over two. 299 00:11:03,797 --> 00:11:05,933 Which is going to be 10 divided by two is five. 300 00:11:05,933 --> 00:11:07,998 So it's going to be five times the square root of 301 00:11:07,998 --> 00:11:10,687 three meters per second. 302 00:11:10,687 --> 00:11:12,539 So if I wanna figure out 303 00:11:12,539 --> 00:11:14,906 the entire horizontal displacement, 304 00:11:14,906 --> 00:11:16,508 so let's think about it this way, 305 00:11:16,508 --> 00:11:19,051 the horizontal displacement, 306 00:11:19,051 --> 00:11:19,884 that's what we get for it, 307 00:11:19,884 --> 00:11:20,879 we're trying to figure out, 308 00:11:20,879 --> 00:11:23,555 the horizontal displacement, 309 00:11:23,555 --> 00:11:25,183 a S for displacement, 310 00:11:25,183 --> 00:11:28,481 is going to be equal to the average velocity 311 00:11:28,481 --> 00:11:32,244 in the x direction, or the horizontal direction. 312 00:11:32,244 --> 00:11:33,787 And that's just going to be this five 313 00:11:33,787 --> 00:11:35,174 square root of three meters per second 314 00:11:35,174 --> 00:11:36,840 because it doesn't change. 315 00:11:36,840 --> 00:11:38,245 So it's gonna be five, 316 00:11:38,245 --> 00:11:40,513 I don't want to do that same color, 317 00:11:40,513 --> 00:11:45,355 is going to be the five square roots of 3 meters per second 318 00:11:45,355 --> 00:11:46,899 times the change in time, 319 00:11:46,899 --> 00:11:49,244 times how long it is in the air. 320 00:11:49,244 --> 00:11:52,402 And we figure that out! Its 1.02 seconds. 321 00:11:52,402 --> 00:11:53,985 Times 1.02 seconds. 322 00:11:55,297 --> 00:11:57,205 The seconds cancel out with seconds, 323 00:11:57,205 --> 00:11:58,503 and we'll get that answers in meters, 324 00:11:58,503 --> 00:12:01,909 and now we get our calculator out to figure it out. 325 00:12:01,909 --> 00:12:06,292 so we have five time the square root of three, 326 00:12:06,292 --> 00:12:07,209 times 1.02. 327 00:12:09,812 --> 00:12:11,812 It gives us 8.83 meters, 328 00:12:13,059 --> 00:12:13,892 just to round it. 329 00:12:13,892 --> 00:12:16,281 So this is going to be equal to, 330 00:12:16,281 --> 00:12:18,698 this is going to be equal to, 331 00:12:19,636 --> 00:12:21,603 this is going to be oh, sorry. 332 00:12:21,603 --> 00:12:24,478 this is going to be equal to 8.8, 333 00:12:24,478 --> 00:12:25,708 is that the number I got? 334 00:12:25,708 --> 00:12:26,541 8.83, 335 00:12:27,710 --> 00:12:28,710 8.83 meters. 336 00:12:29,883 --> 00:12:30,815 And we're done. 337 00:12:30,815 --> 00:12:32,731 And the next video, I'm gonna try to, 338 00:12:32,731 --> 00:12:36,572 I'll show you another way of solving for this delta t. 339 00:12:36,572 --> 00:12:37,405 To show you, really, that there's 340 00:12:37,405 --> 00:12:39,101 multiple ways to solve this. 341 00:12:39,101 --> 00:12:40,269 It's a little bit more complicated 342 00:12:40,269 --> 00:12:42,284 but it's also a little bit more powerful 343 00:12:42,284 --> 00:00:00,000 if we don't start and end at the same elevation.