Concepual Physics Review (Chapers 2 & 3) Soluions Sample Calculaions 1. My friend and I decide o race down a sraigh srech of road. We boh ge in our cars and sar from res. I hold he seering wheel seady, slam on he gas, and my speedomeer shows an increase in speed of 10 meers per second every second. a) Wha is my acceleraion? a "v " v # inal iniial 10m /s # 0m /s 1s 10m /s 2 b) If I mainain ha consan acceleraion, how fas will I be going a he end of 10 seconds? v i + a 0 + (10m /s 2 )(10s) 100m /s c) How far have I raveled in hose 10 seconds? d v avg, and v avg v i + 0 +100m /s 50m /s 2 2 d (50m /s)(10s) 500m OR d v i + 1 2 a 2 0 + 1 ( 10m /s2) 10s 2 ( ) 2 500m 2. Grace is driving her spors car a 30 m/s when a ball rolls ou ino he sree in fron of her. She slams on he brakes and comes o a sop in 3.0 s. Wha was he acceleraion of Grace s car? (Use a posiive sign if she is speeding up, and a negaive sign if she is slowing down) a "v # v i 0 # 30m /s a #10m /s 2 3s 3. A orpedo fired from a submerged submarine is propelled hrough he waer wih a consan speed of 20.00 m/s and explodes upon impac wih a arge 2000.0 m away. a) How long does i ake he orpedo o reach is arge? v d, so d v 2000m 20.0m /s 100s b) If he sound of he impac is heard by he people inside he submarine 101.4 s afer he orpedo was fired, wha is he speed of sound in waer? The orpedo akes 100 seconds o reach is arge. Only hen does i hi he arge, making a sound when i explodes. So, he sound iself ravels all he way back o he submarine in he remaining ime of 1.4 seconds: sound oal " orpedo 101.4 "100 1.4s v d 2000m 1.4s 1429m /s
4. Bobby, a lab, ra has 2.0 minues o go hrough a maze o ge he yummy cheese. He sars off by meandering 100 cm down a pah a a rae of 2.0 cm/s before sopping, sniffing and deciding o go lef or righ. I akes him 10.0 seconds o decide o urn righ. He hen scurries down a 50 cm pah a a rae of 2.5 cm/s before making a lef, speeding up o 3.0 cm/s and racing o he cheese, which is 90 cm away. Does he make i before a rap door crashes down, blocking he cheese? a) Does Bobby ge o ea he yummy cheese? (Show your work) speed disance ime,so disance speed segmen"1 100cm 2.0cm /s 50s & 50cm segmen"3 2.5cm /s 20s segmen"4 90cm 3.0cm /s 30s oal 50s +10s + 20s + 30s 110s 100s 1 # 1min 60s 1.8minues...so, yes, he ges o ea! b) Draw a disance vs. ime graph of he siuaion. Label your axes wih words, unis, and a numbered scale.
5. King Kong carries Fay Wray up he Umpire Sae Building in New Fork Ciy. A he op of he skyscraper, Fay Wray s shoe falls from her foo. I his he ground 15 seconds laer. For his problem, ignore air resisance. a) How fas is he shoe going he insan before i his he ground? v i + a 0 + ("10m /s 2 )(15s) "150m /s The negaive sign indicaes ha he objec is falling down, and is a resul of using -10 m/s 2 for he acceleraion. Afer all, graviy causes objecs o accelerae downward, in he negaive direcion. b) How all is he Umpire Sae Building? Well, how far did he shoe fall during he 15s? d 1 2 a 2 1 2 (!10m / s2 )(15s) 2!1125m or v avg v i+ 0 +!150m / s!75m / s 2 2 d v avg (!75m / s)(15s)!1125m A negaive disance is acually called a displacemen,which is a vecor quaniy. This quaniy is negaive because he objec ends up a a posiion below where i sared. Since he quesion asks how all he building is, i is appropriae o give your answer as a posiive number, 1125 meers. 6. The Seamboa Geyser in Jellysone Naional Park is capable of shooing is ho waer up from he ground wih a speed of 50 m/s. How high can he geyser shoo? Ignore air resisance. We can figure his ou using d 1 a 2 if we can figure ou for wha lengh of ime he waer is in he 2 air. Concepually, you should be able o see ha waer wih an iniial velociy of 50 m/s will slow o 0m/s in 5s, because he acceleraion is -10m/s 2 when i s shooing hrough he air. Or: a " v i,so " v i a 0 " 50m /s "10m /s 2 5s Now, how far does he waer ravel during hose 5s? d 1 2 a 2 1 2 ("10m /s2 )(5s) 2 125m, or d v avg (25m /s)(5s) 125m
7. A Six Flags Grea Advenure Amusemen Park in New Jersey, a popular ride known as Free Fall carries passengers up o a heigh of 33.5 m and drops hem o he ground inside a small cage. How fas are he passengers going a he boom of his exhilaraing journey? Ignore air resisance. To ge velociy, we ll need o know for how long he cage falls, so we have o ge ime firs: d 1 2 a 2, which rearranges o become 2d a 2("33.5m) 2.58s "10m /s 2 Now: v i + a 0 + ("10m /s 2 )(2.58s) "25.8m /s 8. A pop fly is hi sraigh up a an iniial speed of 40 m/s. Ignore air resisance. a) How long is i in he air if i is caugh a he same heigh from which i was hi? There are los of differen sraegies for solving his. Concepually, we know ha i will ake 4 seconds o slow down from 40m/s o 0m/s, a -10m/s 2, and he same amoun of ime o come down, so ha gives us 8 seconds. You can calculae his using a formula as well: " v i a 0 " 40m /s "10m /s 2 4s (for going up) # 2 8s b) How high is i 2 seconds afer i is hi? Velociy afer 2 seconds of going up is 20m/s, so... d v avg " d v + v % i f " 40 + 20% $ ' $ ' 2 60m # 2 & # 2 & c) How high does i go? d v avg " d v + v % i f " $ ' 40 + 0 % $ ' 4 80m # 2 & # 2 & d) Wha is is velociy 6 seconds afer i was hi? Concepually, we know ha he ball is falling back down from is maximum heigh a ime 4 s. Two seconds laer, i has been acceleraing down a 10m/s 2, so i mus be going -20 m/s. Mahemaically: v i + a 0 + ("10m /s 2 )(2s) "20m /s e) How high above is saring poin is i 6 seconds afer i was hi? Well, how far has i fallen from is maximum heigh of 80m during hose 2 seconds? d 1 a 2 1 ("10m 2 2 /s2 )(2s) 2 "20m 80m " 20m 60m above he ground
9. Wrie a descripion of an objec whose moion is represened by he following graph. Be sure o give a chronological descripion, saring wih wha is happening a ime 0. Use appropriae physics vocabulary such as velociy and acceleraion. The objec begins a a locaion 0.5m and sars raveling in 4 he posiive direcion (o he righ). From 0 o 1.5 seconds, 3.5 he objec is speeding up (increasing velociy, or 3 acceleraing posiively here) as i moves in he posiive 2.5 direcion, and hen from 1.5 o 2.5 seconds i appears o be 2 raveling a a relaively consan velociy. Then, from 2.5 o 1.5 4 seconds i begins o slow down (acceleraion in he 1 negaive direcion), sill raveling in he posiive direcion 0.5 bu wih a lesser speed unil i comes o a hal a locaion 0 0 1 2 3 4 5 3.7 meers. posiion x (meers) ime (seconds) 10. Wrie a descripion of an objec whose moion is represened by he following graph. Be sure o give a chronological descripion, saring wih wha is happening a ime 0. Use appropriae physics vocabulary such as velociy and acceleraion. The objec here begins a some locaion wih a posiive velociy vs. ime velociy, bu ha velociy is decreasing over ime 30 (acceleraion, negaive in his case). The objec coninues 20 o lose velociy unil, a ime 5 seconds, i comes o hal 10 for an insan, and hen begins moving again wih a 0 negaive velociy, raveling back he direcion ha i 0 2 4 6 8 10 12 originally came from. Velociy (meers/second) -10-20 -30-40 Time (seconds) The objec has a consan acceleraion, which is o say is velociy is consanly changing. Alhough he acceleraion of he objec in his graph is - 5.0m/s 2, if i were -10 m/s 2, he shape of his graph would be consisen wih a ball ha was hrown up ino he air wih an iniial velociy of 20m/s. Tha ball would decrease is velociy unil i reached an insananeous velociy of 0 a he op of is pah, before saring o fall down wih increasing speed (increasingly negaive velociy). 11. Rochelle is flying o New York for her big Broadway debu. If he plane heads ou of Los Angeles wih a velociy of 220.0 m/s in a norheas direcion, relaive o he ground, and encouners a wind blowing head-on a 45 m/s, wha is he resulan velociy of he plane, relaive o he ground? Draw a picure of he siuaion. 220.0m/s 45m/s 175m/s norheas
12. In her physics lab, Melanie rolls a 10-g marble down a ramp and off he able wih a horizonal velociy of 1.2 m/s. The marble falls ino a cup placed on he floor 0.51 m from he boom of he able. How high is he able? Draw a picure of he siuaion. Horizonal d v d 0.51m 0.43s v 1.2m /s Verical d 1/2a2 ½ (9.8m/s2) (0.43s)2 0.91 m 13. Ber is sanding on a ladder picking apples in his grandfaher s orchard. As he pulls each apple off he ree, he osses i ino a baske ha sis on he ground 3.0 m below a a horizonal disance of 2.0 m from Ber. How fas mus Ber hrow he apples (horizonally) in order for hem o land in he baske? Draw a picure of he siuaion. Verical: d 1/2a2 3.0m ½(9.8m/s2) 2 0.61s2 2 Don forge o ake he square roo of boh sides!!! 0.78s Horizonal: d v v d 2.0m 2.56m /sec 0.78sec
14. A cannon is fired up from he ground a an angle of 53 from he horizonal, wih a velociy of 100 m/s. Draw a picure of he cannon and label he angle of launch and draw he velociy vecor, in he direcion he cannonball will be fired. a. On your diagram above, draw and label he componen vecors (horizonal and verical) for he iniial velociy of a cannonball o be fired from he cannon. Hin: Based on he angle of launch, you can infer ha he righ riangle formed by he wo componen vecors and he resulan is a 3-4-5 righ riangle. This is a 3,4,5 righ riangle, so vx60m/s and vy 80m/s b. How long will i ake he cannonball, afer i is fired, o reach is highes poin? vf vi + g 0 80m/s + (-10m/s2) 8 sec c. How long afer being fired will he cannonball hi he ground? In he absence of air resisance, i akes an equal amoun of ime o go up and come down, so oal ime in he air 2(8 sec) 16 sec. d. How high above he ground is he cannonball a is highes poin? Analyzing from he op down: d 1/2 g2 d ½(-10m/s2) (8sec)2 d -320 m Or, he ball fell 320 m, so he highes poin mus be 320 meers above he ground. e. How far away from he cannon does he cannonball land (horizonal disance)? dx vx (60m/s) (16 sec) 960 m f. In he space below, draw he cannonball a wo-second inervals and draw he horizonal and verical componens of is velociy (vecors) a each wo-second inerval.