Calculus and AnalysisBob wanted to reach the peak of a mountain.
3 months ago
Bob wanted to reach the peak of a mountain.He started at te the base and started driving a car towards the peak of the mountain. The car started at 0 mph and the speed increased over time to 40 mph.Halfway towards the peak of the mountain, the terrain became too rugged and Bob instantly stopped his car to analyze the terrain. After spending time observing the terrain, Bob decided to instantly climb the rocky terrain at a slov pase.Once Bob passed the rocky terrain he realized his shins were cut up so he immediately travelled back to the car at the same slov pace as before. After spending time putting on bandages, he realized there was a side path to the peak of the mountain. He immediately started running to the peak of the mountain and eventually reached the peak. Graph the relationship between Bob's (a) distance and time and (b) position and time. For the graph,make it clear what part of your function corresponds with his different parts of his travels, (Label each segment of your graph)
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ladyantebellumconcertschedule Staff answered 3 months ago
Problem Solution Overview Here, we first need to view this problem in a better way. First thing is to understand a simple thing, that is Speed = Distance / Time This is important, because, this gives us a very important information, as slope of the Distance-Time graph is Slope= Distance / Time = Speed Thus, distance means any movement of bob, which is not necessarily in direction of peak But position means the position of bob with respect to the peak, so when bob started to climb and run through the side path we are talking about his position. Defining the time instances and respective distance and position Let, Initial speed be 0, time =0 and distance = 0 => speed =0 and position = PO T1- time when car reached speed of 40 mph, position = Pi, Distance = D1 T2- time when he reached halfway and stopped the car and started analysing the terrain, position = P2, distance = D2 T3- time when he finished analysis and started climbing, position = P2, distance = D2 T4- time when bob realized that he is injured. Position = P3 and distance = D3 T5- bob reached back to car to put bandages. Position = P2 and distance = D4 T6- bob applied bandages and got to know about side path. Position = P2 and distance = D4 T7- bob reached the mountain peak by running through side path. Position = P4 and Distance = DS
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