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Derivative Problem: Bob the Formula 1 Fan

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Bob is a Formula 1 fan, lucky enough to obtain tickets for the last race of the season, and the tickets are excellent, facing the long straight part of the track, where most of the overtaking occurs. At one point during the race, the race leader reached the top speed of 300km/h, and he was almost in front of Bob when it happened! (see attached picture). How fast was Bob's angle of vision changing when that happened? (In other words, find da/dt for the configuration in the picture.

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Solution Summary

The expert determines how fast Bob's angle of vision changing is happening through using derivatives.

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Solution: Let the instantaneous distance of the car from the position A (just opposite Bob on the track) be x. Then, x/15 = tan a

a = tan-1(x/15) ...(1)

Using the standard differentiation d/dx (tan-1x) ...

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