WEBVTT 00:00:00.000 --> 00:00:03.160 This is Giancoli Answers with Mr. Dychko. 00:00:04.260 --> 00:00:05.940 We want to know the velocity of 00:00:05.940 --> 00:00:07.840 Huck Finn with respect to the river bank 00:00:07.840 --> 00:00:12.100 so we need to add the velocity of Huck Finn with respect to the river 00:00:12.280 --> 00:00:15.120 plus the velocity of the river with respect to the bank 00:00:15.400 --> 00:00:17.500 and the inner subscript's are the same here, 00:00:17.500 --> 00:00:20.460 they are both R—river—and so they disappear 00:00:20.460 --> 00:00:23.580 and we are left with H and B in our answer; 00:00:23.580 --> 00:00:25.900 Huck Finn with respect to the bank which is what we want. 00:00:26.460 --> 00:00:29.320 And so we have the two vectors here that we know; 00:00:29.320 --> 00:00:32.160 one is Huck Finn with respect to the raft— 00:00:32.160 --> 00:00:35.160 0.7 meters per second straight across the river— 00:00:35.160 --> 00:00:37.920 and then we know the velocity of the river with respect to the bank 00:00:37.920 --> 00:00:41.580 which is 1.5 meters per second downstream 00:00:42.560 --> 00:00:46.480 and this red vector is the resultant; 00:00:46.480 --> 00:00:49.940 this is the velocity of Huck Finn with respect to the river bank. 00:00:51.060 --> 00:00:53.560 So the speed or the magnitude of the velocity 00:00:53.560 --> 00:00:56.700 is the square root of the sum of the squares of these two 00:00:56.700 --> 00:00:58.360 velocities here 00:00:58.360 --> 00:01:01.860 so that's the square root of 0.7 meters per second squared 00:01:01.860 --> 00:01:03.800 plus 1.5 meters per second squared 00:01:03.800 --> 00:01:06.460 that gives 1.6553 meters per second 00:01:06.460 --> 00:01:08.360 so that's the magnitude of the velocity. 00:01:08.520 --> 00:01:10.060 And then the direction 00:01:10.220 --> 00:01:13.340 let's say we have Θ in here 00:01:13.340 --> 00:01:16.480 between the resultant and straight across 00:01:16.700 --> 00:01:18.440 that would make tan 00:01:18.640 --> 00:01:22.120 that angle would be the opposite over the adjacent 00:01:22.120 --> 00:01:24.480 and then the angle then is the inverse tangent 00:01:24.480 --> 00:01:26.820 of that opposite 1.5 meters per second 00:01:26.820 --> 00:01:29.760 divided by the adjacent which is 0.7 meters per second 00:01:29.760 --> 00:01:32.760 which is about 65 degrees 00:01:32.940 --> 00:01:36.000 and you have to specify 00:01:36.000 --> 00:01:38.140 what you are measuring your angle with respect to 00:01:38.140 --> 00:01:42.960 because it's equally valid 00:01:42.960 --> 00:01:46.940 I mean it's always valid to measure your angle with respect to whatever you like 00:01:46.940 --> 00:01:49.540 but I could imagine somebody could also 00:01:49.540 --> 00:01:51.800 put an angle here with respect to the river bank 00:01:51.800 --> 00:01:55.680 and that would be the complement of this angle 25 degrees 00:01:55.980 --> 00:01:58.720 but what we have chosen to do here is 00:01:58.720 --> 00:02:01.620 65 degrees with respect to straight across. 00:02:01.980 --> 00:02:05.760 So our answer is velocity of Huck Finn with respect to the bank 00:02:05.760 --> 00:02:07.820 is 1.66 meters per second, 00:02:07.820 --> 00:02:11.280 65 degrees downstream from straight across. 00:02:11.460 --> 00:02:16.020 And I have to say downstream because well, if I just say 65 degrees, 00:02:16.020 --> 00:02:18.260 this would also be 65 degrees here 00:02:19.320 --> 00:02:24.240 and so I have to say downstream whereas this would be 65 degrees upstream.