Problem

You're standing outside on a windless day when ra…

01:27

Problem 41 Hard Difficulty

$\bullet$ Crossing the river, II. (a) In which direction should the motorboat in the previous problem head in order to reach a point on the opposite bank directly east from the starting point? (The boat's speed relative to the water remains 4.2 $\mathrm{m} / \mathrm{s} .$ ) (b) What is the velocity of the boat relative to the earth? (c) How much time is required to cross the river?

Answer

$28.4^{\circ},$ north of east
3.7$m / s$
216$s$

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Physics 101 Mechanics

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Video Transcript

So here is the velocity addition diagram. Um be the loose lass Is velocity off water With respect to art, we be slash is velocity ofthe boat with respect to art on the be slashed ofyou isthe velocity off the boat with respect to water Now we as we can see that we be e is towards east The doubloon is deuce out on and very B's last The bloom has a magnitude ofthe four point to meet Oppa second on DH points towards south. Sorry. Um, artist now by victor tradition They know that v Billy slashed of blue a sequel dough velocity ofthe board with respect to art less velocity off water in the respect of world said this gives velocity off port with respect art to be equal to velocity off port with respect to water minus velocity off water with respect a lot. Now, since this is the right angled triangle with this angle 90 degrees So velocity ofthe board with respect to water on this value, we be slashed a blue this the hyper turns off this right angled triangle. So the magnitude ofthe this velocity should be equal to the square root. Oh, the sound off the squares off the other two sides. From here we can find the magnitude ofthe the velocity off the boat with respect to art which will be given by this value. So I basically squared both the sides and then ah, solved for b Vehbi slash on. We already have the magnitudes for these two Alu. So we plant them into this equation and beget this value to be t 0.7 need up a second. So this is actually and so far fight be Let me do it part in our so for the direction off the B's last w. Since this is a right angle triangle, you know that's Tine Thio will be given by the Papen Nicholas side over the high patents. So this will be magnitude off the loose. Laski over b these Lashley, this is equal door point Si o meter per second. Over. Ah, sorry. Says w and the size of a magnitude of four point to meet up a second. And this is he called the one forward 2.1. This means that Sita will be quite alone. Sign in worse off one over 2.1 and we get this. Well, Noto be 20 gauge point four degree. This means that the velocity vector Ah, the which is the velocity off board with respect to water is, uh, 28.4 degree not off east. Now, for the last part, we have to find the time. So we have given the bit off the river, which is d and this is equal to 800 meter. So the time taken toe across the board is the time taken to travel this distance. So this time will be distance over the velocity in that direction. So that is the bass slash Eat. It is velocity off the board with respect to art. And we're just taking the magnitude. Really, We don't need the direction because time is a scholar on. We let this value that we found in part B in this equation and they get time to be equal to select someone for that. So get this time across the river, Toby. 216 seconds

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