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Answer Key Chapter 6 - Henry County Schools

Answer KeyPhysics: Principles and ProblemsSupplemental Problems Answer Key87 Chapter busy waitress slides a plate of apple piealong a counter to a hungry customer sit-ting near the end of the counter. The cus-tomer is not paying attention, and theplate slides off the counter horizontally at m/s. The counter is m long does it take the plate to fallto the floor? y-direction:vyi20, myf5yi1vyit2gt205yi102gt2t5!}2gyi} 5! far from the base of the counterdoes the plate hit the floor?x-direction:vxi m/s, mxf ( m/s)( s) are the horizontal and verticalcomponents of the plate s velocity justbefore it hits the floor? m/svertical:vyf5vyi2gt502( m/s2)( s)5 is on his way out to go groceryshopping when he realizes that he has lefthis wallet at home, so he calls his wife,Yolanda, who opens a high window andthrows DuWayne s wallet down at an angle23 below the horizontal.

Answer Key Physics: Principles and Problems Supplemental Problems Answer Key 89 Method Two: Find v yf component just before the ball hits the wall. v yf, wall 5 v yi 2 gt wall 5 vi sin ui 2 gt wall 5 (21.0 m/s) sin 40.0° 2 (9.80 m/s 2)(1.43 s) 5 2 0.515 m/s

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Transcription of Answer Key Chapter 6 - Henry County Schools

1 Answer KeyPhysics: Principles and ProblemsSupplemental Problems Answer Key87 Chapter busy waitress slides a plate of apple piealong a counter to a hungry customer sit-ting near the end of the counter. The cus-tomer is not paying attention, and theplate slides off the counter horizontally at m/s. The counter is m long does it take the plate to fallto the floor? y-direction:vyi20, myf5yi1vyit2gt205yi102gt2t5!}2gyi} 5! far from the base of the counterdoes the plate hit the floor?x-direction:vxi m/s, mxf ( m/s)( s) are the horizontal and verticalcomponents of the plate s velocity justbefore it hits the floor? m/svertical:vyf5vyi2gt502( m/s2)( s)5 is on his way out to go groceryshopping when he realizes that he has lefthis wallet at home, so he calls his wife,Yolanda, who opens a high window andthrows DuWayne s wallet down at an angle23 below the horizontal.

2 Yolanda throwsthe wallet at a speed of m/s, and thewallet leaves her hand at a height mabove the ground. How far from the base ofthe house does the wallet reach the ground?y-direction:vyi5vi sin ui 5( m/s) sin ( )5 m/syf5yi m1( m/s)t2( m/s2)t2 This is a quadratic equation in the form ax21bx1c50, with a5}12}( m/s2)5 , b5 , and positive solution is sx-direction:vxi 5vicos uixf5xi1vxit5xi1vi cos m1( m/s)cos( )( s) skateboarder is slowing down at a rate m/s2. At the moment he is moving forward at m/s, he throws a basketballupward so that it reaches a height of m,and then he catches it at the same level itwas thrown without changing his positionon the skateboard. Determine the verticaland horizontal components of the ball svelocity relative to the skateboard whenthe ball left his :vyf25vyi222g(yf2yi)yi50, and, at the highest position, vyf 5005vyi222gyfvyi 5 2gyfw5 2( )w( mw) m/s2( )6 ( )224w( )( )w}}}}}2( )1}21}22( m)}} m/s21}21}2 Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, find the time the ball is in the air:yf5yi 1vyit2gt2 Falling from the highest point, vyi 50,yf 50, and yi m05yi102gtdown2tdown5!

3 }2gyi} 5! st52tdown52( s) sx-direction:Distance the skateboarder moves:xs 5xsi1vxsit1at2501( m/s)( s)1( m/s2)( s) mHorizontal distance the ball moves:xb5xbi1vxbit501( m/s)( s) mxb1 Dx5xsDistance skateboard lags behind m5 mHorizontal velocity skateboarder mustthrow ball relative to skateboard:vxi55} }5 m/s opposite the direction ofmotion of the tennis ball is thrown toward a verticalwall with a speed of m/s at an angleof above the horizontal. The horizon-tal distance between the wall and the pointwhere the tennis ball is released is m. what height above the point ofrelease does the tennis ball hit the wall? x-direction:vxi5vi cos ui5xf5xi1vxitxf2xi 5vxitt5}xfv2xixi}5}vxicfo2sxui1} sy-direction:vyi5vi sin uiyf5yi1vyit2gt2yf2yi 5vyit2gt25vi sin ui(t)2gt25( m/s) sin ( s)2( m/s2)( s) the tennis ball already passed thehighest point on its trajectory when ithits the wall?

4 Justify your Answer . Method One: Find the time to maximum height. vyf 5vyi2gtAt maximum height, vyf5005vyi2gtt5}vgyi}5}visginu1}5thighes t5 sFrom part a, sSince , the ball has already passed the highest pointwhen it hits the wall.( m/s) sin }}} m/s21}21}21}21} m}}}( m/s) cos Dx}t1}21}22( m)}} m/s21}21}2 Answer Key88 Supplemental Problems Answer KeyPhysics: Principles and ProblemsCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, 6 continuedAnswer KeyPhysics: Principles and ProblemsSupplemental Problems Answer Key89 Method Two: Find vyf component just before the ball hits the , wall5vyi 2gtwall 5vi sin ui2gtwall5( m/s) sin 2( m/s2)( s)5 m/sSince vyf,wall ,0, the ball is on its waydown and has already passed the high-est Moon revolves around Earth in a circu-lar orbit with a radius of Ittakes days for the Moon to completeone orbit around Earth.

5 What is the cen-tripetal acceleration of the Moon?ac5}vr2}5}4Tp22r}T5( days) }4Tp22r} clown rides a small car at a speed of 15 km/h along a circular path with a radiusof m. is the magnitude of the centripetalforce on a ball held by theclown? m/sFc5mac5m}vr2}5( kg) the point where the car is headed duenorth, the clown throws the ball verti-cally upward with a speed of m/srelative to the moving car. To wheremust a second clown run to catch theball the same distance above the groundas it was thrown?y-direction:vyf 5vyi 2gtAt the highest point, vyf 50thighest5}vgyi}ttotal 52thighest 5}2vgyi}x-direction:R5vxit5}vxgi2yi} m north of the point wherethe clown threw the ball is attached to the end of acord of length m. The ball is whirled ina circular path in a horizontal plane. Thecord can withstand a maximum tension N before it breaks.

6 What is the maxi-mum speed the ball can have without thecord breaking?Fnet 5 macFT5 m}vr2}v5 ! }FmTr}vmax5 ! }FT,mmaxr}5 ! 5 13 moving sidewalk at an airport has aspeed of m/s toward the departure man is walking toward the departuregate on the moving sidewalk at a speed of m/s relative to the side-walk. What is the velocity of the manrelative to a woman who is standing offthe moving sidewalk? vm/w 5 vm/s1vs/gr 1vgr/w vgr/w5 m/s, since the woman is standing still( N)( m)}}( kg)( m/s)(2)( m/s)}}} m/s2( m/s)2}} m1 h}3600 s1000 m}1 km15 km}1 h4p2( )}}}( )23600 s}1 h24 h}1 dayCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, 6 continuedvm/w5 m/s5 m/s toward the departure a similar moving sidewalk that is going in the opposite direction, a childwalks toward the terminal at a speed of m/s relative to the sidewalk.

7 Whatis the velocity of the man relative to the child?vm/c5 vm/s11vs1/gr 1vgr/s21vs2/cvgr/s25 vs2/grvs2/c 5 2vc/s2vm/c 5vm/s11 vs1/gr 2vs2/gr2vc/s25 m/s2( m/s)2( m/s)5 m/s toward the departure a sightseeing trip in Europe, Soraya is riding in a tour bus moving northalong a straight section of road at m/s. While Soraya looks out at a forest, shehears some passengers on the other side of the bus say they can see a famous cas-tle from their side. Soraya hurries straight across the bus, going east at m/srelative to the bus, so that she also can see the castle. What is Soraya s velocityrelative to the castle?vS/c5 vS/b1 vb/cvS/c5 vS/b1vb/cvS/b5 m/s, vb/c 5 m/s, vS/c5 ?Because the two velocities are at right angles, use the Pythagorean theorem:vS/c25 vb/c21vS/b2vS/c 5 vb/c21wvS/b2w5 ( mw/s)21w( mw/s)2w5 m/s u5tan211}vvSb//cb}25tan211} }25 27 vS/c 5 m/s at 27 east of northNE vS/bvb/cvS/cAnswer Key90 Supplemental Problems Answer KeyPhysics: Principles and ProblemsCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, 6 continuedAnswer KeyPhysics: Principles and ProblemsSupplemental Problems Answer kite is tethered to a stake on a beach.

8 The wind has a constant velocity of 16km/h at an angle of 15 from the horizontal relative to the beach. Find the com-ponents of the kite s velocity relative to the ,w5vwcos uvy,w5vwsin uvk/w5vk/b1vb/wvb/w5 2vw/b5 2vwvk/w5 vk/b2 vwvx,k/w5vx,k/b2 vx,w5vx,k/b2 vwcos km/h 2(16 km/h)(cos 15 )5 215 km/hvy,k/w5vy,k/b2 vy,w5vy,k/b2 vwsin km/h 2(16 km/h)(sin 15 ) 5 marble rolls off the edge of a table that is m high. The marble is movingat a speed of m/s at the moment that it leaves the edge of the table. How far from the table does the marble land?df2di5vi1at2vi50 and a5 2gDd 5 2gt2t5! Ris the range which is equal to vxitR5vxi5vxi! 5vxi! 5( m/s) 1! m22( m)}}} m/s222(df2di)}}g22Dd}g22Dd}g1}21}2 Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, 6 and Carmen are playing catch with aflying disk when it gets stuck in a tree.

9 Thedisk is lodged between two branches mabove the ground. If a rock is thrownstraight up to hit the disk, what is the minimum speed with which the disk mustbe thrown?vf25vi212awDd vf50 and a5 2g05vi222gDdvi5 2gDdw5 2( )w( mw)w513 baseball player is playing catch with hisfriend. When the ball leaves his hand it ismoving at m/s. He throws the ball atan angle of above the horizontal. Hisfriend catches the ball at the same heightfrom which it was thrown. How far is thebaseball player from his friend?vfy5viy1atvfy50 m/s anda5 2g05viy2gtt5}vgiy}5}visginu} sttotal52t52( s) sDd5vxiDtDt5ttotalDd5(vicos u) ttotal5( m/s)(cos )( s) car moving at m/s rounds a bendin the road. The bend is semicircular and has a radius of m. What is the centripetal acceleration of the car? town has a large clock on the hall in thetown square. The clock has hands that showthe hours, minutes, and seconds.

10 A fly is sitting on the tip of the hand that shows theseconds. If the length of the hand is m,what is the fly s centripetal acceleration? rock is tied to a string and spun in a hori-zontal circle. The string is m long andthe rock has an acceleration of is the tangential velocity of the rock?ac5v5 acrw5 ( mw/s2)( m) airplane flies north at km/h relative to the air and the wind is blowingsouth at km/h. What is the airplane svelocity relative to the ground?vp/g5vp/a1 km/h 1( km/h) km/h northwardv2}r4p2( m)}}( s)24p2r}T2( m/s)2}} mv2}r( m/s) sin }}} m/s2 Answer Key92 Supplemental Problems Answer KeyPhysics: Principles and ProblemsCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, 6 continu


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