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(I) Huck Finn walks at a speed of 0.70 $\mathrm{m} / \mathrm{s}$ across his raft (that is, he walksperpendicular to the raft's motion relative to the shore). The raft is traveling down theMississippi River at a speed of 150 $\mathrm{m} / \mathrm{s}$ relative to the nver bank(Fig. $49 ) .$ What is Huck's velocity direction) relative to the river bank?

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$25^{\circ}$ relative to river

Physics 101 Mechanics

Chapter 3

Kinematics in Two or Three Dimensions; Vectors

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Simon Fraser University

University of Sheffield

McMaster University

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the question states that hook thin walks at a speed of 0.70 meters per second. Across his wrath, that is, he walks perpendicular to the rafts motion relative to the shore. The raft is traveling down the Mississippi River at a speed of 1.50 meters per second per second. Relative to the riverbank, Figure 49. What is Huck's velocity, speed and direction relative to the riverbank? I wrote down here what we were given in the question and that is that the velocity of Huck Finn, which I write his Visa H 0.70 meters per second. And since that has both magnitude and direction, I denote the direction as J hat and the velocity of the raft is perpendicular to J hat. So I called that the eye hat direction in that velocity, which I ran. His visa bar is 1.50 meters per second. Also draw a little graph here, showing what we know, which is the direction of the velocity of Huckleberry Finn, as well as the direction of the velocity of the raft and we're trying to find is the direct the velocity of Huck Finn relative to the riverbank. So the riverbank I'm gonna just right. This is green. Says the riverbank over here. So you want the direction relative to the riverbank? Okay, which I write is the redline V H Prime for the prime version of hook. Very fense velocity relative to the riverbank and then fatal, which is the direction. So magnitude and direction is what we're going to try to find. So VH Prime here is write this out is equal to the velocity of the raft. Great plus velocity of Huckleberry Finn. Okay, call that is equal to 1.50 I had plus 0.70 Jay. Okay. Oh, and these were both meters per second. So I could put that on the outside. Well, since one is in the eye, had direction and one is in the J hot direction. We cannot add those together, but we can't find their magnitude, which is what we were asked to find. So the man two of the h prime She can write the magnitude as thes VH Prime with these bars around it, that represents magnitude is equal to the square of what I'm trying to square root of the sum of the square of both sides that make it up. So this would be the r a squared plus create square Hillary Something square root here. Since then, you know that. Okay, so if we plug in those values, we find that this is swear it. Those 1.50 squared plus 0.70 squared. Of course, this is in meters per second. We put these in, we find that this equals 1.66 meters per second. Clarke said in that's our magnitude. But we weren't just asked to find magnitude were also asked to find direction so we can use the trigger metric tight. And I'm gonna ride it next to the graph here where the tangent the fada is equal to the office it over the high part nous that angle. So the opposite would be Visa Beach and it stops over. And Jason, I'm sorry. Not ops, overhype, oddness of ease, of age and that Jason is a piece of our Okay, so we're gonna use that relationship to find data so few not going back down here. If you solve for theta, data is equal to the inverse tangent, and she could write this tangent to the minus one of the H O. V E. R. We'll just plug in the values for those. So that's going to be zero 0.70 divided by me or from plants I zero and the meters per second unit's Cancel something. I'm gonna worry about that. So if you take the inverse tangent of that value, you find this equals 25 degrees okay from that 25 degrees and we'll just take this how is relative to the direction of the raft or the direction of the bank? Because the draft moves perpendicular or a parallel to the bank? Okay. And we can go hand box set in a czar solution for the direction, So you solved both magnitude and direction.

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