The police are investigating a crime that took place in Galloping Gulch at 7 pm on Thursday, November 19. A woman riding a horse was seen by several witnesses in the area of the crime scene around the time that the crime was committed, and the police want to determine if she could have committed the crime. They have access to the following data about the speed of the horse from the rider’s cell phone (which you may assume is accurate and has not been falsified by the rider). t 0 0.1 0.2 0.3 0.4 0.5 v(t) 36 33 30 2 17 9 In the data above, t is time (in hours) after 7 pm on the day of the crime, and v(t) is the speed of the horse (in kilometers per hour). You may assume that the horse traveled in one direction over the entire time period and that the speed of the horse always decreased. (a) Find an overestimate and an underestimate of the distance traveled by the horse between 7 and 7:30 pm. Show your work, include the proper units with your answer, and make it clear which answer is which. (b) After interviewing several witnesses, the police have concluded that the rider of the horse was 12 kilometers away from Galloping Gulch at 7:30 pm. You have been hired as a mathematical consultant, and it is your job to write a report to the police concerning whether or not the rider of the horse should be considered a suspect. Your report should be long enough to address the following: the meaning of your calculations from part (a) and how you know that they represent over and underestimates of the distance traveled, whether or not the rider could have committed the crime and whether or not there is reasonable doubt that she could have committed it, and exactly how you used your calculations to reach your conclusions. Your report should be written in a form that is appropriate to your audience, meaning that it should explain the meaning of the mathematics in layman’s terms.
The police are investigating a crime that took place in Galloping Gulch at 7 pm on Thursday, November 19. A woman riding a horse was seen by several witnesses in the area of the crime scene around the time that the crime was committed, and the police want to determine if she could have committed the crime. They have access to the following data about the speed of the horse from the rider’s cell phone (which you may assume is accurate and has not been falsified by the rider).
| t | 0 | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 |
| v(t) | 36 | 33 | 30 | 2 | 17 | 9 |
In the data above, t is time (in hours) after 7 pm on the day of the crime, and v(t) is the speed of the horse (in kilometers per hour). You may assume that the horse traveled in one direction over the entire time period and that the speed of the horse always decreased.
(a) Find an overestimate and an underestimate of the distance traveled by the horse between 7 and 7:30 pm. Show your work, include the proper units with your answer, and make it clear which answer is which.
(b) After interviewing several witnesses, the police have concluded that the rider of the horse was 12 kilometers away from Galloping Gulch at 7:30 pm. You have been hired as a mathematical consultant, and it is your job to write a report to the police concerning whether or not the rider of the horse should be considered a suspect. Your report should be long enough to address the following: the meaning of your calculations from part (a) and how you know that they represent over and underestimates of the distance traveled, whether or not the rider could have committed the crime and whether or not there is reasonable doubt that she could have committed it, and exactly how you used your calculations to reach your conclusions. Your report should be written in a form that is appropriate to your audience, meaning that it should explain the meaning of the mathematics in layman’s terms.
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