STEM5-math 108 - Math Learning Center Boise State 2010...

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Math Learning Center Boise State ©2010 Linear Modeling STEM Last week we looked at momentum problems, g G ±² . Consider the following problem: If a 3000kg truck traveling at 5 m/s strikes a 2000 kg sedan which is stopped at a stop light and if the two vehicles stick together (moving as one) what is the speed of the two vehicles after the collision? Ignore friction. The law of Conservation of linear momentum states that the sum of the momentum of the two vehicles before the crash is equal to the momentum of the two vehicles after the crash. To accomplish this problem, we will use subscripts to distinguish between the truck (t) and the sedan (s) before the crash and the combined vehicles (c) after the crash. Hence are variables are: g ³ ´ µ¶±·¸¹º± ¶» ¹¼· ½¶±¾¿¸À ²·¼¿½Á·Â û¹·Ä ¹¼· ½Äü g Å ´ µ¶±·¸¹º± ¶» ¹¼· ¹Äº½Æ ¾·»¶Ä· ¹¼· ½Äü g Ç ´ µ¶±·¸¹º± ¶» ¹¼· ·Àø ¾·»¶Ä· ¹¼· ½Äü ± ³ ´ µÃ ¶» ¹¼· ½¶±¾¿¸·À ²·¼¿½Á·Â G uUUU ÆÈ É ÊUUU ÆÈ G ËUUU ÆÈ ± Å ´ µÃ ¶» ¹¼· ¹Äº½Æ G uUUU ÆÈ ± Ç ´ µÃ ¶» ¹¼· ·Àø G ÊUUU ÆÈ ² ³ G Ìg··À ¶» ¹¼· ½¶±¾¿¸·À ²·¼¿½Á·Â û¹·Ä ¹¼· ½Äü Íμù Ï· ÃÄ· Á¶¶Æ¿¸È »¶ÄÐ ² Å ´ Ìg··À ¶» ¹¼· ¹Äº½Æ G Ë ±Ñ ² Ç ´ Ìg··À ¶» ¹¼· ·Àø G U ±Ñ This problem has more letter representations than most at the math 108 level which is why we need the subscript to assist us in distinguishing the variables while at the same time still allowing the letters to represent momentum, mass and velocity. When working a word problem the first step is to list the symbols that will be used and if you know the values to list them. Thus, we have completed the first step to solve this problem. The second step is to identify what we are looking for, which we have also completed – Combined Velocity - ² ³ Ò Next we identify the equations we know using ² ³ (and we insert known values where possible: g ³ G ± ³ ² ³ g ³ G ËUUU² ³ From this equation, we can determine ² ³ , if we know g ³ . Thus, let us look for equations that might help us find g ³ Ò Based on the law of conservation of momentum, we know that g ³ G g Å É g Ç From last week, you should be able to find both g Å ÓÔÕ g Ç Ò Thus, we will allow you to finish the problem from here and determine ² ³ Ò
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Math Learning Center Boise State ©2010 We have used the word crash in the problem to help visualize the move into forensic science and the mathematics needed to develop an understanding of an accident scene by only looking at the end
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STEM5-math 108 - Math Learning Center Boise State 2010...

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