SPH3U: Projeciles Now i s ime o use our new skills o analyze he moion of a golf ball ha was ossed hrough he air. Le s find ou wha is special abou he moion of a projecile. Recorder: Manager: Speaker: 0 3 4 5 A: Tracking a Projecile. Observe. Choose a convenien reference poin on he ball o help rack is moion. Measure he x- and y-componens of he posiion of he ball a each momen in ime. The coordinae sysem for your measuremens is drawn on he picure. The srobe ligh for he phoo flashed a 0 Hz. Complee he char below. Image No. (s) d x (cm) d y (cm) 3 4 5 6 7 8 9 0 B: Horizonal Moion. Represen. Plo a graph of d x vs.. Reason. Refer o he paern of daa represened in he graph. Wha ype of moion does he projecile experience in he x-direcion? d x (cm) 8.0 6.0 3. Analyze. Use an appropriae graphical echnique o deermine he horizonal componen of he velociy, v x. 4.0.0 4. Represen. Use he graph o help creae an equaion ha represens he horizonal posiion of he ball. Be sure o include unis and don use he symbols x and y! 0 0 0. 0.4 0.6 0.8.0 (s) 5. Reason. Use he daa of he graph o explain wheher here is any significan evidence for forces acing in he horizonal direcion? Wha can we conclude abou he effecs of air resisance? C. Meyer, 0
6. Apply. If he ball moved for a oal 5.0 s, wha would is horizonal posiion be? Par B: Verical Moion. Represen. Plo a graph of d y vs.. Reason. Refer o he paern of daa in he graph o help explain wha ype of moion he ball experiences in he verical direcion. d y (cm) 8.0 6.0 4.0.0 0 0 0. 0.4 0.6 0.8.0 (s) 3. Explain. A suden says ha he is no sure why he graph for quesion represens acceleraion downwards. Explain wihou referring o any forces. 4. Represen. Skech a v y- and an a y- graph based on he d y- graph. Line up he graphs feaures wih he d y- graph above. Label he regions in ime when he ball is speeding up, slowing down and has a verical speed of zero. C: Projecile Moion. Summarize. Use he observaions you have developed o creae a model of projecile moion. Your model should begin by explaining ha we rea he objec as a poin paricle. Describe he characerisics of he paricle s verical and horizonal moions and menion any assumpions he model relies upon. Projecile Moion:. Apply. According o your model, will he projecile ever be found falling sraigh down? Explain. 3. Predic. Two projeciles are launched wih he same iniial speeds bu differen angles. Marie launches hers wih an angle of 60 o o he horizonal and Alber launches his a an angle of 30 o o he horizonal. According o your model, whose projecile will spend more ime in he air? Explain. We will es his using a simulaion. Marie Alber 4. Speculae. How migh our undersanding of projecile moion change if air resisance is an imporan facor?
SPH3U: Projecile Problem Solving The key idea which allows us o solve projecile problem is he independence of he horizonal and verical moions. Since he verical physics does no affec he horizonal physics, we can rea a single projecile problem as wo relaed kinemaics Recorder: Manager: Speaker: 0 3 4 5 problems one for each direcion. When we se up our work, i is helpful o organize he givens ino separae groups for he horizonal and verical aspecs of he problem. A convenien way o show he direcion of he velociies used o describe projecile moion is o simply indicae he angle and use a sign convenion wih posiive for above he horizonal and negaive for below. For example: m/s [3 o ] or 50 km/h [- o ]. A: The Ski Jump The ski jump is an exciing and deah-defying even ha urns humans ino projeciles! sudy he physics of he crazies winer spor as feaured a he Vancouver Winer Olympics in 00. Le s A ypical ski jumper will be launched wih a speed of 6 m/s. Wha is hard o noice picures is ha he launch angle is below he horizonal! For he Vancouver hills, he was.5 o below he horizonal. v from angle. Represen. Begin all your projecile moion problems by drawing a skech and creaing a char lising wha you know abou he horizonal and verical moion. Include a sign convenion. Find componens of any known vecors.. Explain. Explain wha seps are involved in finding he jumper s verical velociy afer a ime inerval. Horizonal Verical v x = v y = d x = v y = a x = a y = = d y = = he 3. Solve. Deermine he jumper s oal velociy vecor afer.8 s of fligh. 4. Evaluae. Is your resul reasonable (size, unis, direcion)? Explain. C. Meyer, 0 3
5. Represen. Draw a moion diagram and skech he d- and v- graphs for he x- and y- componens of he jumper s moion. Draw he vecors v, v and v in such a way ha we can see how hey are relaed. Explain beside he vecors. Moion Diagrams Posiion-ime Graphs Velociy-ime Graphs Vecors + x d x v x d y v y + y 6. Explain. The jumper ravels beyond he.8 s and soon lands afer descending a cerain verical displacemen d y. Based on he saring informaion of his problem, explain how o find he horizonal displacemen of he jumper. 7. Calculae. The jumper descends 35.8 m. How far horizonally did she ravel? 8. Reason. Emmy says, I hink he calculaion above would have been easier if we had used he fac ha v y = 0 since she has landed. Do you agree wih Emmy? Explain. 9. Reason. In a compleely differen siuaion involving a ski jumper, he following equaions were arrived a: d x = (.5 m/s) d y = (0.3 m) + (.5 m/s) + ½(-9.8 m/s ) Creae a carefully worded exbook problem for hese equaions. Given your problem saemen, a suden should arrive a exacly hose equaions during he soluion. Be creaive! 4
B: The Grea Jumper Sondre Norheim (85 897) was a ski jumping champion and he designer of he modern ski used for ski jumping. The modern ski acs like a wing, providing he jumper wih an upwards lif force. In our work here, for simpliciy, we ignore all effecs of he air and his upwards force. The sory goes ha Sondre wowed a group of specaors by jumping over a very all rock. Le s explore he physics of his daredevil even. We will suppose ha he launched from a ramp wih a speed of 8.0 m/s a an angle of 8 o above he horizonal. The edge of he ramp was.5 m above he ground level. The alles poin of he rock was locaed 3.8 m horizonally from he edge of he ramp and was 5.0 m above he ground. The ground in his area is quie level.. Represen. Skech his scene and consruc a lis of horizonal and verical givens. Include a sign convenion.. Reason. Our goal is o deermine wheher or no he would make i over he rock. Wha kinemaics quaniy would i be helpful o find (and compare wih he given informaion) ha would allow you answer his quesion? Explain carefully. 3. Explain. Describe he seps necessary o solve his problem. 4. Calculae. Perform he calculaion solve for your unknown quaniy. 5. Evaluae. Inerpre he resul of your calculaion and sae he oucome of his problem. 6. Calculae. The ground under he ramp is level. How far horizonally does he ravel while in he air? 5