Sample Problems. Lecture Notes Motion Problems page 1

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1 Lecture Notes Motion Problems page 1 Sample Problems 1. We traveled for nine ours. Ten we increased our velocity by 10 les per our and traveled an additional ve ours. Wat was our original velocity if all togeter we ave traveled 750 les? 2. A bicycle leaves Cicago, eading East at 10. Cicago, eading East at 12 bicycle? Tree ours later, a second bicycle leaves. How long will to take for te second bicycle to overtake te rst 3. Town A and town B are located 55 les apart. A jogger starts in town A and jogs toward town B. At te same time, a bicycle starts in town B and travels toward town A. Te di erence between te speed of te jogger and tat of te bicycle is 3 les per our. Find te speeds if te jogger and te bicycle meet exactly 5 ours after te start. 4. Ann eaded sout at 35 les per our. Two ours later Sue followed er, at 45 les per our. How long until Sue catces up wit Ann? 5. Te cop was casing te crook wo ad a 100 ft ead start. Te velocity of te cop was 15 feet per second wile tat of te crook was 11 feet per second. How long until te cop catces up wit im? 6. A plane leaves an airport and ies sout at 300 les per ours. Later, a second plane leaves te same airport and ies sout at 450 les per our. If te second plane overtakes te rst one in 1 our, ow muc earlier did te rst plane leave? 7. Cicago, IL and Montpelier, VT are about 1000 les apart. A car leaves Cicago to Montpelier at te same time as a train leaves Montpelier for Cicago. Te train is 50 faster tan te car. Find te speed of te car if it takes 5 ours until te train and car meet. 8. A bicycle leaves Cicago, eading East at 14. Cicago, eading East at 17 bicycle? Tree ours later, a second bicycle leaves. How long will to take for te second bicycle to overtake te rst 9. Milwaukee, WI and Albuquerque, NM are about 1500 les apart. A plane leaves Milwaukee to Albuquerque at te same time as a train leaves Albuquerque for Milwaukee. Te plane is 330 faster tan te train. Find te speed of te plane if it takes 3 ours until te plane and train meet. c copyrigt Hidegkuti, Powell, 2008 Last revised: January 27, 2009

2 Lecture Notes Motion Problems page 2 Practice Problems 1. We traveled for nine ours. Ten we increased our velocity by 7 les per our and traveled an additional six ours. Wat was our original velocity if all togeter we ave traveled 582 les? 2. A bicycle leaves Cicago, eading East at 12. Two ours later, a second bicycle leaves Cicago, eading East at 15. How long will to take for te second bicycle to overtake te rst bicycle? 3. Town A and town B are located 68 les apart. A jogger starts in town A and jogs toward town B. At te same time, a bicycle starts in town B and travels toward town A. Te di erence between te speed of te jogger and tat of te bicycle is 5 les per our. Find te speeds if te jogger and te bicycle meet exactly 4 ours after te start. 4. Ann eaded sout at 45 les per our. Two ours later Sue followed er, at 55 les per our. How long until Sue catces up wit Ann? 5. Te cop was casing te crook wo ad a 60 ft ead start. Te velocity of te cop was 14 feet per second wile tat of te crook was 9 feet per second. How long until te cop catces up wit im? 6. A plane leaves an airport and ies sout at 400 les per ours. Later, a second plane leaves te same airport and ies sout at 480 les per our. If te second plane overtakes te rst one in 1 our, ow muc earlier did te rst plane leave? 7. Cicago, IL and Montpelier, VT are about 1000 les apart. A car leaves Cicago to Montpelier at te same time as a train leaves Montpelier for Cicago. Te train is 40 faster tan te car. Find te speed of te car if it takes 5 ours until te train and car meet. 8. A bicycle leaves Cicago, eading West at 15. Two ours later, a second bicycle leaves Cicago, eading West at 20. How long will to take for te second bicycle to overtake te rst bicycle? 9. Milwaukee, WI and Albuquerque, NM are about 1500 les apart. A plane leaves Milwaukee to Albuquerque at te same time as a train leaves Albuquerque for Milwaukee. Te plane is 120 faster tan te train. Find te speed of te plane if it takes 3 ours until te plane and train meet. c copyrigt Hidegkuti, Powell, 2008 Last revised: January 27, 2009

3 Lecture Notes Motion Problems page 3 Sample Problems - Answers ours ours and seconds nutes earlier ours and 415 Practice Problems - Answers ours after te second bicylce started 3. Te speed of te jogger is ours and tat of te bicycle is seconds ours our or 12 nutes earlier 9. Te speed of te train is 190 and tat of te plane is 310 c copyrigt Hidegkuti, Powell, 2008 Last revised: January 27, 2009

4 Lecture Notes Motion Problems page 4 Sample Problems - Solutions 1. We traveled for nine ours. Ten we increased our velocity by 10 les per our and traveled an additional ve ours. Wat was our original velocity if all togeter we ave traveled 750 les? 50 Solution: Let us denote our velocity in te rst nine ours by x. trip our velocity was x v t ( ) s ( ) Part 1 x 9 9x Part 2 x (x + 10) During te second part of te Te distance traveled in te rst part and te distance traveled in te second part add up to 750 les. Tus te original velocity was 50. 9x + 5 (x + 10) = 750 9x + 5x + 50 = x + 50 = A bicycle leaves Cicago, eading East at 10. Cicago, eading East at 12 bicycle? 15 ours 14x = 700 x = 50 Tree ours later, a second bicycle leaves. How long will to take for te second bicycle to overtake te rst Solution: Let x denote te time tat te second bicycle spent traveling. ad x + 3 ours to travel. v t ( ) s ( ) bicycle 1 10 x (x + 3) bicycle 2 12 x 12x Ten te rst bicycle Te distances are equal. Tey bot start at Cicago and meet at te meeting point. 10 (x + 3) = 12x 10x + 30 = 12x 30 = 2x 15 = x Tus it will take 15 ours after te second bicylce started. c copyrigt Hidegkuti, Powell, 2008 Last revised: January 27, 2009

5 Lecture Notes Motion Problems page 5 3. Town A and town B are located 55 les apart. A jogger starts in town A and jogs toward town B. At te same time, a bicycle starts in town B and travels toward town A. Te di erence between te speed of te jogger and tat of te bicycle is 3 les per our. Find te speeds if te jogger and te bicycle meet exactly 5 ours after te start. 4 and 7 Solution: Let x denote te speed of te jogger. Ten te speed of te bicycle is x + 3. v t ( ) s ( ) jogger x 5 5x bicycle x (x + 3) Te equation expresses tat wen tey meet, te jogger and te bicycle as covered te 55 les between A and B. Tus te speed of te jogger is 4 5x + 5 (x + 3) = 55 5x + 5x + 15 = 55 10x + 15 = 55 10x = 40 x = 4 and tat of te bicycle is Ann eaded sout at 35 les per our. Two ours later Sue followed er, at 45 les per our. How long until Sue catces up wit Ann? 7 ours Solution: Let x denote te time tat Sue as traveled, measured in ours. Since se started two ours earlier, Ann traveled for x + 2 ours. v t ( ) s ( ) Ann 35 x (x + 2) Sue 45 x 45x Te distances are equal. 35 (x + 2) = 45x 35x + 70 = 45x 70 = 10x 7 = x Tus it will take 7 ours until Sue catces up wit Ann. c copyrigt Hidegkuti, Powell, 2008 Last revised: January 27, 2009

6 Lecture Notes Motion Problems page 6 5. Te cop was casing te crook wo ad a 100 ft ead start. Te velocity of te cop was 15 feet per second wile tat of te crook was 11 feet per second. How long until te cop catces up wit im? 25 seconds Solution: Let x denote te time tey bot ad to travel. ft v t ( s) s ( ft) s crook 11 x 11x cop 15 x 15x Te cop ad to run as muc as te crook ran, in addition to te eadstart. Tus it will take 25 seconds. 11x = 15x 100 = 4x 25 = x 6. A plane leaves an airport and ies sout at 300 les per ours. Later, a second plane leaves te same airport and ies sout at 450 les per our. If te second plane overtakes te rst one in 1 our, ow muc earlier did te rst plane leave? 30 nutes earlier Solution: Let x denote te time tat te rst plane traveled before te second plane started. Ten te faster plane traveled for one our, and te slower on as traveled x + 1 our unti tey meet. v t ( ) s ( ) slower plane 300 x (x + 1) faster plane Te equation expresses tat wen tey meet, te distances traveled by ta planes are equal. 300 (x + 1) = x = x = 150 x = x = 1 2 Tus te rst plane left 1 2 our (or 30 nutes) earlier. c copyrigt Hidegkuti, Powell, 2008 Last revised: January 27, 2009

7 Lecture Notes Motion Problems page 7 7. Cicago, IL and Montpelier, VT are about 1000 les apart. A car leaves Cicago to Montpelier at te same time as a train leaves Montpelier for Cicago. Te train is 50 faster tan te car. Find te speed of te car if it takes 5 ours until te train and car meet. 75 Solution: Let x denote te speed of te car, measured in les per our. Ten te speed of te train is x velocity time ( ) distance ( ) car x 5 5x train x (x + 50) Te equation expresses tat te distances traveled are equal. Ten te speed of te car is 75. 5x + 5 (x + 50) = x + 5x = 1000 subtract x = 750 divide by 10 x = A bicycle leaves Cicago, eading East at 14. Cicago, eading East at 17 bicycle? 14 ours Tree ours later, a second bicycle leaves. How long will to take for te second bicycle to overtake te rst Solution: Let us denote by x te time it took for te second bicycle to overtake te rst bicycle. Ten te oter bicycle ad x + 3 ours, since it started tree ours earlier. velocity time ( ) distance ( ) slower 14 x (x + 3) faster 17 x 17x 14 (x + 3) = 17x 14x + 42 = 17x subtract 14x 42 = 3x divide by 3 14 = x so it takes 14 ours for te second bicycle to overtake te rst bicycle. c copyrigt Hidegkuti, Powell, 2008 Last revised: January 27, 2009

8 Lecture Notes Motion Problems page 8 9. Milwaukee, WI and Albuquerque, NM are about 1500 les apart. A plane leaves Milwaukee to Albuquerque at te same time as a train leaves Albuquerque for Milwaukee. Te plane is 330 faster tan te train. Find te speed of te plane if it takes 3 ours until te plane and train meet. 85 and 415 Solution: velocity time ( ) distance ( ) train x 3 3x plane x (x + 330) Tus te speed of te train is 85 3x + 3 (x + 330) = x + 3x = x = x = 510 x = 85 and tat of te plane is 415. For more documents like tis, visit our page at ttp:// and click on Lecture Notes. questions or comments to degkuti@ccc.edu. c copyrigt Hidegkuti, Powell, 2008 Last revised: January 27, 2009