solutionshomework2(2014) - Jan 24 2014 Homework#2 Due(next...

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Unformatted text preview: Jan. 24, 2014 Homework #2 Due: (next) Friday, Jan. 31 Read Chapter 2 Solve the following problems: (You will be graded on your method of solution as well as your answer, so be sure to show your work.) 1. A ball rolls across the floor of the lecture hall in a straight line at a constant velocity v = 5.0 m/s in the positive a; —direction. Its motion is timed with a stopwatch. Initially (when the stopwatch is started) its a: — coordinate is $1 = 1.2 111. When the stopwatch is stopped some time later, its (a — coordinate is $2 = 3.4 m. (a) What is the displacement Arc in this time interval? (b) What is the elapsed time At on the watch? (c) Make a graph showing 9; vs t, with a; in meters and t in seconds. (You can download free graph paper from the site http://incompetech.com/graphpaper/) ((1) Write down an equation for a; as a function of t, and use your equation to predict the :L' coordinate of the ball after 2.0 s assuming that it has not yet bounced off the wall. 2. A car is driven in a straight line at a constant velocity 1) = 40 km/hr in the positive 1‘ direction. After some time the driver reaches his destination, a distance of 10 km from the starting point. At this point he quickly turns the car around and resumes the journey with a constant velocity v : ~60 km/ hr. Eventually he arrives back at the starting point. (a) What is the time for the round trip? (b) What is the time—average velocity for the round trip? (c) What is the time—average speed for the round trip? (d) How do your answers to b & c change if the destination is instead 20 km away? 30 km? 3. The graph below shows the velocity of a particle moving in the :1: direction as a function of time. You can see that the velocity is a constant 5 m/s. If initially a: = 0, then after an elapsed time of 1 second, the particle will have moved 5 meters. This distance is indicated by the shaded area on the graph, a box that has the correct dimensions of meters, which you can see by multiplying widthxheight => SX % 7:111. (a) Suppose that we want to know the distance the particle has moved after 2 seconds, What shaded area would correspond to this distance? (b) Finishing filling out the data table below showing 93 vs to m(m) t(s) 0 0 5 1 10 2 (5- 3 20 4 2f 5 .30 6 (0) Use the table in (b) to finish putting the seven points on the graph below showing 9: vs t. (d) What is the equation of the straight line giving 12 as a function of t on the 1) - t graph. What is the equation of the straight line giving as as a function of t on the m — t graph? 4. The graph below shows the velocity of a particle moving in the :0 direction as a function of time. You can see that the velocity is a constant 5 m/s for the first 1 second, and then abruptly jumps to 10 m/s and remains so for the second second, and then You can see that the velocity is a constant 5 m/s for the first 1 second, and then abruptly jumps to 10 m/s and remains so for the second, and then abruptly jumps again to 15 m/s, etc. If initially it = 0, then after an elapsed time of 1 second, the particle will have moved 5 meters. (a) Suppose that we want to know the distance the particle has moved after 2 seconds. What shaded area would correspond to this distance? (b) Finishing filling out the data table below showing :0 vs t. 31(m) t(s) 0 0 5 l 15 2 30 2 {9 if” 5 513 W Z 30$ 6 (c) Use thewtabflle in (b) to finis putting the seven points on the graph below showing :0 vs t. ‘ i i A » i ”gun“. is “a (d) A parabolic equation of the form m = not —l— %‘at2 will pass through all of the points on your :1: vs t graph if the two parameters, the acceleration, a, and the initial velocity 110, are chosen appropriately. Find the values of a and no that work. 5. A car starts from rest and accelerates at a rate of 2.0 m/s2 in a straight line until it reaches a speed of 20 m/s. Then the car slows down at a constant rate of 1.0 in/s2 until it stops. How much time elapses from start to stop? How far does the car travel? l i i ii, 6. As soon as the stop light changes from red to green, a car at rest at the intersection accelerates with a constant accelaration of 2.2 m/sz, At the same moment, a truck passes by, moving at a constant speed of 9.5 In/s. How far beyond the intersection will the car catch the truck? How fast will the car be going at this point? ’ 7. A man steps off a 100 in diving platform. How long will it take him to drop the first 50 in? How long will it take him to drop the second 50 m? 8. When a bullet leaves the barrel of a rifle, it is moving 640 m/s. If the barrel is 1.20 m long, and if the bullet undergoes constant accelaration while within the barrel, how long after the rifle is fired will the bullet emerge from the end of the barrel? 9. Lifeguard David Hasselhoff is standing 100 Hi from the water’s edge when he spots a nonswimmer 100 meters from the shore in need of rescuing. Unfortunately, he is 500 in down athe beach from the swimmer and all of his rescue equipment is being used to make a movie. His top running speed is 15 mph, and his top swimming speed is 3.5 mph. (a) Suppose that David runs diagonally to a point on the shore perpendicular to the swimmer, and then enters the water and swims 100 in. How long will it take him to reach the victim? (b) Suppose that David runs 100 meters directly to the water, jumps in the water, and then swims the remaining distance to the victim along a diagonal path? How long will this take? (c) Suppose that David runs along a diagonal path to the shore, and then swims along a different diagonal path to the Victim. Find, by trial and error using your calculator, or otherwise, the overall path that will give the shortest time, and calculate this time. r 10. A superball is dropped from rest from» a height of 2.0 1n. It bounces repeatedly from the floor, as superballs are prone to do. After each bounce the ball dissipates some energy, so eventually it comes to rest. The following pattern is observed: After the lst bounce, the ball returns to a maximum height that is 3/4 of its initial height. After the 2nd bounce, the ball returns to a maximum height that is 3/4 of its maximum height after the lst; After the 3rd bounce, the ball returns to a maximum height that is 3/4 of its maximum height after the second, etc. In fact, for this particular ball, the maximum height achieved after the nth bounce is found to be 3/4 of the maximum height attained in the previous bounce. If this pattern is repeated, how many times will the ball bounce before coming to rest, and how long the process take? (Neglect air friction.) , Wm. mfghngfiuméf éjEEZ _. w "M m , W 1% 4, ,wwm M ”.‘f ”3—“.pm 4. w E m 2 Fix a 2:23??? g ~ ~ H wwfi E Z Mi. _ (b) , m :2 £2me 1M Mm? , ELMW my H M m ”mm W“ m M, _ , - , M fl , n. W fl- w.“ fl - EE A ., «Eifimm « (3 EMS “_ M fl" ” W _ M w- WE w .. , ”W '"Zfifimg W” w W l h E a i gm? 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Yaw. ,g.4irxsee%mMBAa/JL\J«M-M§flhmmc H , 4,4me ; x 75. aha-MA: fly] M We ~---~p4/V11MJ: 14M 4mg fl «3170:»! -/3?- J‘ - i . ! 1%, pp [email protected] <V© @fllVLL<<O>>©[email protected] ~~A>><<o?-I_L’I‘A© C 0° memo >AAq; L1! GNUPLOT ,V .1 If you don’t have a quick way to make a graph using your personal computer, I 1 i 4 would suggest that you download the free program gnuplot. The web page is pasted 1‘; E below. Below this you will see what the command window looks like when the program é is running, and the very simple commands that were issued to make a graph of the lifeguard problem, followed by the resulting graph—-. I have pasted these screen—dumps into a word document, which I have appended to the solutions to homework #1. sinc<xtx+§tw Demos and Screenshots Documentation Links Contributed scgp’ ts and files Tutorials Fm'gg help Builg'ng from cvs source More on Batchg’ g and build_m' g Gnuplot is a portable commandnline driven interactive data and fimction plotting unity for UNIX, IBM 0312, MS Wmdom, DOS, Macintosh, VMS, Atari and many other platfoms. The soflware is copyrighted but freely distributed you don't have to pay E'o ). It was ' y imaended as to allow scientists and students to visualize onnv 221111.00 Es-mzncmww-T:~raw—.z-rwxmwwzwmrrz—zxTmmmw-xmnmmr w 1......» '..r-.r:~:~ G H n P L 0 T HS—uindows 32 bit version 3.? patchleuel 1 (+1.2.fl 2831/91/11) last modified Fri Oct 22 13:ma=ma BET 1999 Copyright<c> 1986 — 1993. 1998, 1999 Thomas Hilliams. Colin Kelley and many others Tfipe help‘ to access the on—line reference manual ”nu lot PRO is available from 9 (http://www. ucc. ie/gnuplnt/gnuplot-faq.html) Send comments and requests for help to (infom maglutfldartmouth.e Send hugs, suggestions and mods to (hug-gnuplot artmouth.edu> Mimi» :ng MW... 'W, WmVK 9...»; . vb «MM». ~11: E: I E 1 E E E E E i E' E E E E: Eflerminal type set to ’uindows’ Egnup plot) f<x>=s qvt((1flfl)**2+(59I-x)**2)/6. 71+sqrt<<1lfl)**2+x**2)/1. 56 E snap lot) set xrange [0: 58] Egnuplot) plot f(x) Egnuplot) E E 1 140.4 140.2 140 139.8 139.3 , 139.4 139.2 139 138.8 138.6 138.4 Wwfl‘w m 2‘ 2?? K x <3nfaywtmflWKAVMWWWW/A» My” firm? «A— K mi.” ,‘_‘,., Mwwwfl W4 MW WNW xaflI7:1:I7QQ,§;;f]j.7§IE};I:Iii;i7 qu/fi i“ r W” 1% 7' «*"fl‘m‘fl" H ,_,,, man-vi .-, ..~. «w ,_,_, WV, w» W. V.“ V, W. ‘ < mugnmw gamma, ma .,£n}g%xvv2g> ,, ...
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