*Problem: The velocity of an object fired directly upward is given by V = 80 – 32t, where t is in seconds. When will the velocity be between 32 and 64 feet per second? solution: I will set up the compound inequality, and then solve for t: 32 < 80 – 32t < 64 32 – 80 < 80 – 80 – 32t < 64 – 80 –48 < –32t < –16 –48 / –32 > –32t / –32 > –16 / –32 1.5 > t > 0.5 Note that, since I had to divide through by a negative, I had to flip the inequality signs. Note also that you might (as I do) find the above answer to be more easily understood if written the other way around: 0.5 < t < 1.5 Looking back at the original question, it did not ask for the value of the variable t, but asked for the times when the velocity was between certain values. So the actual answer is: The velocity will be between 32 and 64 feet per second between 0.5 seconds after launch and 1.5 seconds after launch. Always remember when doing word problems, that, once youve found the value for the variable, you need to go back and re-read the problem to make sure that youre answering the actual question. The inequality 0.5 < t < 1.5 did not answer the actual question regarding time. I had to interpret the inequality and express the values in terms of the original question.
Posted on: Thu, 30 Jan 2014 17:45:11 +0000
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