The position of a squirrel running in a park is given by r = [(0....

Question

The position of a squirrel running in a park is given by r = [(0.280 m/s)t + (0.0360 m/s2)t2]î + (0.0190 m/s3)t3ĵ. (b) At t = 5.00 s, how far is the squirrel from its initial position?

Accepted Answer

Hey everyone welcome back in this problem. We are given the position of a hypothetical quirk in subatomic space. Okay. And it's given here by s equals 1.414 T plus 0.136 t squared all times I hat plus 0. 60 cube times J hat. Alright. And we're asked to find how far this hypothetical cork is from its initial position after four seconds. Okay. We're given information with the units. So the function is an angstrom. So 10 to the minus 10 m and our time is in seconds. Alright. So we have the position s that were given. We're just going to rewrite that at 1.141 T plus 0.136 t squared I hat. 0.0796 T. Cubed J. Hat. And we're told we're looking for the position after four seconds. Okay so let's go ahead And substitute t equals to four seconds. Okay we're gonna get s equals 1.414 times four plus 0.136 times four squared All times. I have plus zero .0796. Many times for cute. And then we have R. J had at the end. Okay, so simplifying we are going to have 5.656 plus 2.176. I have plus 5. jihad. Okay, simplifying that first term 7.832 I hat plus 5.0944. Jr Alright so we know after four seconds. This is the position we are at. The particle is at. Okay. And we want to find what how far we are from our initial position. Okay, so recall that the I hat and J hat are unit vectors, Katie I had as a unit vector in the X direction. The positive extraction to the right and jihad in the positive Y direction up. Okay. So what this tells us is that if this is our initial point here we're moving to the right Or the Cork has moved to the right 7. to the in the right direction. And it has also moved up 5.944. Okay, so again the extraction given by this unit vector I hat in the Y direction. By the unit vector J. Hat. Okay, so our change in position is gonna be this quantity here. Okay, well we have a right triangle so we can just use pythagorean theorem. So we can call this D. Our distance K D squared is equal to 5.944 squared plus 7.832 squared KD Squared equals 87.293. Taking the square root D. Is going to be plus or minus 9.3431. Okay, and in this case we are looking for a distance we're looking for how far so we don't need to concern ourselves with the negative here. We only want the positive. So we're just gonna say 9.3431. And the units were told in the question here are angstrom. So we're gonna put the symbol here for that. Okay, And that's our answer. Okay, So that's how far the hypothetical quark moved from its initial position. That's answer. B. Thanks for watching. See you in the next video.

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