OBJECTIVES Students should e ale to: 1 Calulate the horizontal and vertial omponents of a veloity vetor given the initial vetor. 2 Define givens as eing either horizontal or vertial. 3 Plae appropriate S.I. units on all givens and answers. 4 Calulate the apogee of any projetile motion. 5 Calulate the time in the air for any projetile motion. 6 Calulate the impat SPEED of any projetile motion. 7 Calulate the time to any given height in a projetile s motion. Honors A B Calulate the impat veloity (magnitude and diretion) Calulate the veloities angle and speed at any given loation in a projetile s path. Find the vertial and horizontal omponents for eah of the veloities given elow. 1. A rok is thrown with a speed of 46.5 m/s at an angle of 38 with the ground. 2. A Volvo lands after driving off a liff at an angle of 68 with the ground. It impated the ground at 32 m/s. 3. An alien spae-egg is atapulted from the planet Ork at an angle of 75 with the ground and a speed of 459 m/s. 4. A meteor hits the Earth with a speed of 86 m/s at an angle of 21 with the ground. 5. A girl jumps off a swing and lands at 7 m/s and at an angle of 39 with the ground. 6. A jet lands on an airraft arrier with a horizontal speed of 109 m/s and a downward vertial speed of 9.0 m/s. What is the VELOCITY (Magnitude and Diretion) of the jet? Symmetrial Projetile Motion 7. Mike Kester threw a javelin at 57 m/s and at an angle of 25 degrees with the ground. Neglet the height of the javelin when it was thrown. a. How high did the javelin travel?. How long was it in the air?. How far along the ground did the javelin travel? d. How fast, (diretion and magnitude), was it traveling when it hit the ground? 8. An arrow is shot up at a 37 angle with the horizontal. The Arrow leaves the ow traveling 68 m/s. a. How high aove the ground did the arrow travel? Neglet the height of the ow from the ground when shot.. How long was it in the air? Another fine worksheet y T. Wayne - 1 -
. How far aross the ground did it travel? 9. The motoryle dare-devil Evil Kinevil is aout to make a world reord distane jump. He leaves the jump ramp at 45m/s. The ramp is at a 22 angle with the ground. He lands at the same height he took off from. a. How high does he travel?. How long is he in the air?. What is the distane of his jump? d. what is his veloity when he lands? 10. Evil Kinevil is aout to make another world reord distane jump. He leaves the jump ramp at 45m/s. The ramp is at a 68 (90-22 ) angle with the ground. He lands at the same height he took off from. a. How high does he travel?. How long is he in the air?. What is the distane of his jump? d. what is his veloity when he lands? 11. A spear is thrown with veloity of 30 m /s at a 34 angle with the ground? Neglet the initial height the spear was thrown from. a How far did the spear travel? How long was the spear in the air? How high did the spear travel? 12. A dare devil stunt man travels off a jump with veloity of 50 m /s at a 20 angle with the ground? The stunt man lands at the same height he took off from. a How far away should the landing ramp e plaed? How long was the motoryle dare devil in the air? How high did the motoryle dare devil travel? 13. A aseall player ats a all with a veloity of 60 m /s at an angle of 80 with the ground. a How far did the all travel? How long was the all in the air? How high did the all travel? d A aseall player from the opposing team is standing 30 m from where the all is going to land. What average speed does the player have to run to ath the all? 14. Typially an assault rifle shoots a ullet at 1000 m /s. The rifle is aimed at 10.0 and the ullet lands on the ground. Neglet the height the ullet was shot from. a How far did the ullet travel? How long was the ullet in the air? How high did the ullet travel? 15. Not knowing any etter, Tom hit Jerry with a tennis raquet. Jerry left the raquet with a veloity of 60 m /s at a 75 angle. a. How muh time passes efore Jerry hits the ground?. How high does Jerry travel?. How far along the ground does Jerry travel? d. How fast is Jerry traveling when he hits the ground? e. How far along the ground will Jerry travel if he is launhed at a 15 angle with the ground at 60 m /s? f. What is the relationship etween 75 and 15? g. Who are Tom and Jerry? Another fine worksheet y T. Wayne - 2 -
16. In a footall game, a quarterak throws a all to a reeiver. The quarterak takes the hike from the enter. 3.0 seonds later he passes the all with a veloity of 20 m /s at a 30 angle with the ground. a How high did the all travel? How long was the all in the air? How far down the field did the all travel? d What speed will the all hit the ground with and at what angle? e With what average veloity will the reeiver have to run with in order to ath the all the moment it gets to the ground? 17. While traveling down the road, a driver loses ontrol of his ar the ounes off a ur at a 8.5 angle with the ground. The ar lands at the same height is takes of from. The ar was traveling 40.0 m /s when it ouned at 8.5. a How long was the ar in the air? How far did the ar travel? What veloity did the ar impat the ground with? (magnitude AND diretion) 18. Waldo Walenda, one of The Flying Walenda's, was swinging on a trapeze. He let go of the trapeze when it was traveling 20.0 m /s at a 40.0 angle with the vertial. Waldo is to ath another trapeze that is at the same height as the one he left. When he athes the other trapeze it is to e at the end of its swinging motion. Try to rereate the situation using these questions as a guide. a. How long was Waldo in the air?. How high aove the trapeze did Waldo travel?. How far from the trapeze was the waiting trapeze (Horizontal distane)? d. If the waiting trapeze has a length of 6 meters, at what time -relative to the moment when Waldo lets go of the trapeze- does the waiting trapeze need to e released? V o is Horizontal 19. In a movie Borris Badenough is pushed horizontally out of a window. He exits the window horizontally at 5.0 m /s. Borris lands 15 m from the edge of the uilding. a. What is the Borris Badenough s initial horizontal veloity?. What is the Borris Badenough s initial vertial veloity?. How fast, vertially, is the Borris traveling when it hits the ground? d. How long was Borris in the air? e. How high was the window Borris fell from? f. What SPEED did he impat the ground? g. What VELOCITY did he impat the ground? (magnitude AND diretion). 15 m Uh oh... Another fine worksheet y T. Wayne - 3 -
20. A penny is kiked horizontally off the roof of a 10 story uilding (33.3 m high). It is kiked at 22 m/s. a. What is the penny's initial horizontal veloity?. What is the penny's initial vertial veloity?. How long is the penny in the air? d. How far away from the uilding did the penny land? e. What is the penny s SPEED when it hits the ground? f. How fast, vertially, is the all traveling when it hits the ground? g. How fast, horizontally, is the penny traveling when it hits the ground? h. What is the penny's VELOCITY (magnitude and diretion) when it hits the ground? 21. A all is rolled horizontally out a seond story window (7 m high) with a veloity of 10.0 m /s. a. What is the all's initial horizontal veloity?. What is the all's initial vertial veloity?. How long is the all in the air? d. How far away from the uilding did the all land? e. What is the all s SPEED when it hits the ground? f. How fast, horizontally, is the all traveling when it hits the ground? g. How fast, vertially, is the all traveling when it hits the ground? h. What is the all's VELOCITY (magnitude and diretion) when it hits the ground? 22. The Wile E. Coyote was hasing the Road Runner when he ran horizontally off a liff at 46 m /s. Wile E. Coyote is falling for 12 seonds efore hitting the ground. a. How high is the liff?. How far from the edge of the liff did the oyote travel efore hitting the ground?. What was the oyote's impat SPEED d. What was the oyote's impat veloity, (MAGNITUDE and DIRECTION)? 23. The Charlottesville parking garage on Market Street is 6.0 stories high, 19.8 m. A ar travels horizontally off the top of the garage at 2.2 m/s, (5 mph. ) a How far from the edge of the uilding did the ar land? How long was the ar in the air? With what speed was the ar traveling when he hit the ground? d What veloity did the ar impat the ground? (magnitude AND diretion) 24. A student is at a quarry and attempting to run off the edge of a liff. They run off the liff at horizontally at 10 m/s. The edge of the liff is 5 m aove the water. a How far from the edge of the uilding did the student land? How long was the student in the air? With what speed was the student traveling when he hit the water? d What veloity did the student impat the ground? (magnitude AND diretion) Another fine worksheet y T. Wayne - 4 -
V o is an angle and x & x o are not equal 25 45 m/s 26 25 m 25 X =? A stunt rider is making a motoryle jump. Through a planning error the landing ramp s end does not math the take-off ramp s height. The landing ramp is 25 m high. The take off ramp is 10 meters high at the end. a. Where should the ramp e plaed (x)?. How long is the rider in the air? A skier was traveling 20 m/s when they hit a hill and launhed themselves up into the air at a 30 angle. They hit a tree when they were at the highest part of the motion. a How long was the skier in the air? How high did the skier travel? #@*%& How far along the ground did the skier travel? $! 27. A rok is thrown off a tall uilding at 45 m/s at an angle of 30 elow the horizontal. a. How long is the rok in air?. How far from the uilding did the rok land?. What is rok s veloity (magnitude and diretion) at impat? 30 deg 45 m/s 42 m Another fine worksheet y T. Wayne - 5 -
28. A rok is thrown off a tall uilding at 45 m/s at an angle of 60.0 aove the horizontal. a. How high did the rok travel?. How long is the rok in air?. How far from the uilding did the rok land? d. What is rok s veloity (magnitude and diretion) at impat? 45 m/s 60 50 m 29. The ar rolls off the liff with V = 31 m/s 37 60 m How long is the ar in the air? How far from the liff s edge will the ar land? How fast and at what angle will the ar impat the ground? Another fine worksheet y T. Wayne - 6 -
30. A snow all is thrown out a seond story window (7 m high) with a speed of 32 m/s. It is thrown at an angle of 57 eneath the horizontal. a. What is the all's initial horizontal veloity?. What is the all's initial vertial veloity?. How long is the all in the air? d. How far away from the uilding did the all land? e. How fast, vertially, is the all traveling when it hits the ground? f. How fast, horizontally, is the all traveling when it hits the ground? g. What is the all's VELOCITY (magnitude and diretion) when it hits the ground? 31. A Penny is thrown out off the Eifel Tower (303 m high) with a speed of 43 m/s. It is thrown at an angle of 83 eneath the horizontal. a. What is the penny's initial horizontal veloity?. What is the penny's initial vertial veloity?. How long is the penny in the air? d. How far away from the uilding did the penny land? e. How fast, horizontally, is the penny traveling when it hits the ground? f. How fast, vertially, is the penny traveling when it hits the ground? g. What is the penny's VELOCITY (magnitude and diretion) when it hits the ground? 32. While sitting in a tree, Tarzan tried to get a trapper's attention y throwing a anana with a veloity of 20.0 m/s at a 30.0 degree angle eneath the horizontal. a) How high was Tarzan if the anana took 2 seonds to hit the ground? ) With what speed did the anana hit the ground? ) With what angle did the anana hit the ground? 33. Tina, the golfer, tees off the tip-top of a tall turf laden hill. Her golf all is in the air for 6.00 seonds efore oming to a rest 5.00 meters elow the tee's height. a) If the golf is hit with a veloity of 60.00 m/s then what angle was the all hit with? ) How far horizontally did the all travel efore oming to a rest? 34. Tarzan was swinging on a vine when is snapped. At the moment it snapped the vine was 30 from the VERTICAL in an upwards diretion. Tarzan was traveling 25 m /s. Tarzan landed 16 meters along the ground from where the vine roke. a. How long was Tarzan in the air?. How fast was Tarzan traveling when he hit the ground, (MAGNITUDE and DIRECTION)? 35. A rok is thrown at a house with a speed of 30 m/s at an angle of 39 degrees with the ground. If the house is 83 meters away, will the rok hit the house? 36. In a akyard aseall game Billy Bats ats a all eyond the ases. The all is hit at a 58 degree angle with the ground with some yet unknown initial speed. The all travels 235 meters along the ground. a) With what speed does the all hit the ground? ) How long is the all in the air? ) How high did the all travel? 37. At THE odaious mud-og of the year, a ar makes a jump at an angle of 22 degrees with the ground. The truk travels up as high as 5.0 meters. a) What is the truks initial speed when it leaves the ramp? ) How long was the truk in the air? ) How far aross the ground did the truk travel? Another fine worksheet y T. Wayne - 7 -
38. Young Billy Joe Boy Bruey shoots a rok out of a sling shot at an angle of 41 degrees with the ground. The rok travels 78 meters efore hitting the ground. a) What is the rok's initial speed? ) How long is the rok in the air? ) How high did the rok travel? 39. A anon all is fired from a annon that it titled at a 33 angle with the ground. The annon all travels 568 m down range. It also has a vertial veloity omponent of 60.12 m/s. a. How high did the annon all travel?. What was the annon all's initial veloity?. How long was it in the air? 8 REVIEW QUESTIONS COVERING THE DIFFERENT SETUPS 40. While delivering toys Santa Claus slips off the top of a roof. At the edge of the roof he is traveling 12 m/s. a. How long is Santa in the air?. How far from the edge of the house will he land?. With what speed and diretion will Santa impat the ground? 30 12 m/s 7 m 41. A roller oaster ar travels off a hill while traveling downward. a. How long is the roller oaster ar in the air?. How far from the edge of the roken trak will the roller oaster ar?. With what speed and diretion will roller oaster ar impat the ground? 33 Ahhh.. 25 m/s 125 m X =? Another fine worksheet y T. Wayne - 8 -
42. A grape rolls off the top of the leaning tower of Pisa at 9 m/s. The tower is 80 m high and tilts at an 11 angle with the vertial. a. How long is the grape in the air?. How far from the edge will the grape land?. With what speed and diretion will the grape impat the ground? 9 m/s. 43. A dog is in a field athing a frisee. The dog leaves the ground at 7.53 m/s at an angle of 50 with the ground to ath a frisee at his apogee. a. How long was the dog in the air until it aught the frisee?. How far, horizontally, did the dog jump to the loation where he aught the frisee?. How high did the dog jump? 80 m 11 44. Calvin was fliking pennies at Hoes. One of his pennies flew upwards at 5.0 m/s at an 75 angle with the tale top. When it landed, it was 0.75 meters higher than it started. a. How long was the penny in the air?. How far, horizontally, did the penny travel?. How high did the penny travel? d. With what speed and angle will the penny impat the ounter top aross the room? 0.75 m θ =? 45. Little ay Herman threw a green ean upwards with a veloity of 3 m/s at a 30 angle. The ean landed 1.25 meters elow where it was thrown. a. How long was the ean in the air?. How far, horizontally, did the ean travel?. How high did the ean travel? d. With what speed and angle will the ean impat the ground? 1.25 m θ =? 46. A ug, 0.06 kg, ounes upwards off a windshield while traveling 55 mph, 26.5 m/s. The ug ounes at a 37 angle with the horizontal. The ug hit the windshield of a truk ehind the ar at a height of 0.82 m aove the oune. a. How long was the ug in the air?. How far, horizontally, did the ug travel?. How high did the ug travel? d. With what speed and angle will the ug impat the windshield? Another fine worksheet y T. Wayne - 9 -
47. While hasing the Road Runner, Wile E. Coyote makes wrong turn and ends up sliding horizontally off the edge of a high liff. He leaves the edge of the liff while traveling 55 m/s. The liff s edge is 1505 m aove a anyon floor. a. For how muh time was the oyote in the air?. Horizontally, how far did the oyote travel efore impating the anyon floor?. With what speed and angle did the oyote impat the anyon floor? Another fine worksheet y T. Wayne - 10 -
1 2 3 4 5 6 7 a PHYSICS ANSWERS 8 a 9 a 14.5 m 3.44 s 143.53 m d 45 m/s @ 22 10 a 88.82 m 8.52 s 143.54 m d 45 m/s @ 68 11 a 85.14 m 3.42 m 14.36 m 12 a 13 a 14 a 15 a e f g 16 a e Another fine worksheet y T. Wayne - 11 -
17 a 18 a 19 a PHYSICS 28 a 29 a 30 a ANSWERS e f g 20 a e f g 31 a e f g 21 a 10 m/s 0 m/s 1.20 s d 11.95 m e 15.4 m/s f 10 m/s g 11.71324 m/s h 15.4 m/s 22 a 705.6 m 552 m 126.28 m/s d 126.28 68.64 w/ the ground 23 a 4.42 m 2.01 s 19.82 m/s d 27.86 m/s @ 83.63 w/the ground 24 a 25 a 26 a 27 a e f g 32 a 33 a 34 a 35 36 a 37 a 38 a 39 a Another fine worksheet y T. Wayne - 12 -