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2 A dart is thrown horizontally with an initial speed of 10 m/s toward point P, the bull's-eye on a dart board. It hits at point Q on the rim, vertically below...

Question

2 A dart is thrown horizontally with an initial speed of 10 m/s toward point P, the bull's-eye on a dart board. It hits at point Q on the rim, vertically below P, 0.2 s later. What is the distance PQ? How far away from the dart board is the dart released?Find the angle of elevation of a gun which fires a shell with muzzle velocity 366 m/s at a target on the same level but 4,575 m distant:

2 A dart is thrown horizontally with an initial speed of 10 m/s toward point P, the bull's-eye on a dart board. It hits at point Q on the rim, vertically below P, 0.2 s later. What is the distance PQ? How far away from the dart board is the dart released? Find the angle of elevation of a gun which fires a shell with muzzle velocity 366 m/s at a target on the same level but 4,575 m distant:



Answers

A dart is thrown horizontally with an initial speed of $10 \mathrm{~m} / \mathrm{s}$ toward point $P,$ the bull's-eye on a dart board. It hits at point $Q$ on the rim, vertically below $P, 0.19 \mathrm{~s}$ later. (a) What is the distance $P Q ?$ (b) How far away from the dart board is the dart released?

So we can say, with the origin being the initial point, the why coordinates of the dart would be given by negative 1/2 g t squared. And in this case, this is given that the initial Y velocity is zero meters per second. Given that the dart is initially thrown perfectly horizontally and so with why equaling negative P. Q. We consider a distance from point P two point Q is equaling, 1/2 multiplied by 9.8 meters per second, squared multiplied by 0.19 seconds. Quantity squared. And so this is giving us 0.1 eight meters. This would be our answer for part a and then for part B to find the exposition. This would be the initial velocity in the ex direction multiplied by tea, and in this case this would be 10 meters per second multiplied by 100.19 seconds. This is going to give us 1.9 meters for the exposition. That is the end of the solution. Thank you for watching

So this tells that um a person throws a dart with a speed of 10 meters per second and is directed at POINT P. But it actually hits point Q. And that is down below P. It strikes the time to reach. It Is 0.19 seconds. What is the distance from P. To Q. Well, why Rather the changes why is just gonna be 1/2 G. T. Square? So using the calculator Where v. Sub zero is 10 and T. is .19, Then 1/2 g. T squared would be ah 58 centimeters. Okay. How far away from the dartboard was the player? Well, X equals V. Zero times T. That's it. So the zero times T. Is 1.9 m away. Mhm. Mhm. Thank you for watching. Oh, shoot Just a minute. I had g in here as a 32.2. It's supposed to be 9.81. This is metric here. All right. That changes. Uh Delta Y. Is only going to be 18 centimetres and now X Is going to uh still 1.9 m that did not depend on gravity. All right. So, I had gravity as in as 32 0.2 ft per second square. But I needed to write it as 9.81 m per second squared. Alright, thanks for watching

Next election is a function of time, so X relation is a function of time is equal to zero iChat minus 9.81 g camp. And indeed, roll off a T T is equal to the lost is a function of time, which is equal to by 10 co sign Peter. I can't minus 9.2 20 list, then sign Leader G Cap. And also integral off read E T. Is equal to position is a function of time, which is equal to 10. Call sign Peter T. I. Cat minus nine Point Asari four point. It's for 4.905 t's creator Less, uh, again. Sign Preda Times t in the Jacob direction Now distance along X time STI is equal to 10 course I in Peter multiply by t and see the point for Cinque Leader is equal to t that Miss Crowe down well, distance along. Why multiply? Every t is equal to zero, which is equal to minus 4.905 to 0.4 ah sec pleader old square bliss. 10 scientific data into zero point for well sank Lita carbon. This is equal to minus 7.8 for eight. Ah, sex, Sex with Peter List for Dan Pita. And this can before they're returnees minus 9.1962 minus 0.196 to 10. Squared feeding doubtless stand pita now licked you musical to 10 feet up. Then we have here. Zero is equal to minus 0.1962 You square less U minus 0.1 962 Now using ah quality forever. We have huge physical too. 0.2044 and also full. Want to eat 924 So Dante A is equal to 4.89 to 4 and Pita is able to see him into H going for five degrees right now. Uh, since we have unseat a 0.4 sank freedom, multiply by. Sorry. All right, this is equal to feta, right? Is it a point for, uh, 0.4 60 days equals t hide. So t is equal to zero point for multiply by sex, feta. And today's so indeed wind for 54 times you go to 1.99 seven before second. What can no velocity is a function off D and Peter eyes equal to we have, but then go sign off. 78.45 degree lesson two minus 9.8 wanting to 1.9974 less, then sign off. 78 point for fight Right? So this is equal to 2.3 in the I Can't direction minus 9.7971 Indo Jake and Direction and the magnitude of the Lost Isa Musical to root 2.3 square blessing to minus nine point 7971 cold screen, which is equal to 10.0 zeal meter per second.

Well, uh, we have X relation factor. Extradition is a function of time is equal to is your eye camp. So there is no X relation in the I kept direction minus 1.81 J cap. We have four seconds clear. Oh, in giggle or a d t is equal to V is a function of time which is equal to 10. Go sign Peter. I can't. Minus 9.81 dimes D list 10. Sign Peter on Jacob. Right. An integral off bt t is equal to position. It's a function of time which is equal to 10 go scientific data times t I can't minus for wind 1905 r T square Let's 10. Sign Peter A multiply by D uh, she cap right? No, we have our distance along X multiply by D is equal to four. Target is equal to 10 times or sign of Peter multiply V t let miss across town. And was it a blind, fuller sick Peter is equal to t right? No. Our distance along Why our multiply by t is equal to zero Cand zero equals minus four 0.905 into Zito blind for sank Peter Sick Peter won't square less. Then sign Peter. Uh, then scientist a into the wind for Secretaria. I was in a bind for San Kapita right, which is equal to minus leader 0.7 gate for age sex 848 Sex Square Peter Less for damn Peter, right? And the skin before the region is, uh, minus easy to find. 1962 into one Bliss stance Credit Pita want list in Square Leader, um are into Let's Dan Peter Right and part of the skin. Brittanee's minus minus busy defined. 1962 minus little 0.1962 Dan Screen Peter Live Stand Peter Bliss Dan Pita. I'll let you physical too Can Pita Then we have, uh, insead or is equal to minus student 0.196 to you Square lis U minus 0.1 962 And solving this quadratic equation U is equal to, uh, see the point. Busy defined too. Zito for Fuller and damn Peter is equal to 0.20 or for water. So Peter is equal to 11.55 degrees right now. Uh, since Zito find Waller sec feed I is equal to D and he is equal to positive point. Fuller. Ah, time SEC Leader P days 11.55 degrees. So t is equal to zero point or 083 2nd now been lost. He is a function of diamond. Pita is equal to 10. Go sign Peter ICAPP Lesson two minus nine. Going to each one times t this, then sign Peter J Cap right S o B. When time is the client to zero floor for and Peter size 11.5 degrees, then B is equal to 10 cause sign off. 11.5 degrees in the ICAP direction. Artless into minus 9.81 into t well, to you sit a 0.20 for four less. Uh, 10. Sign off. Peter TD's 11. Find five O. J. Cap. So believes equal to 9.7 nine eight ICAPP. This is nice. Sorry. This is seven nine point nine. Boring. Seven 98. This is night 99 camp minus the 990.0 Do mine. Three floor J camp. So magnitude off we is equal to nine point 79 Eat. I mean for a second


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