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Answer :
We wish to find the stopping distance for a car traveling at 35 mph. Although only two data points are provided (for example, a stopping distance of 17.9 ft at 20 mph and 31.8 ft at 50 mph), we know that stopping distance tends to increase with speed in a nonlinear way. In this situation we can use physical reasoning and elimination of unreasonable options to make an estimate.
Here is one way to think about the problem:
1. Notice that the distances given for 20 and 50 mph do not change at a constant rate with speed, so a simple linear relationship is unlikely. In fact, in many stopping‐distance problems the distance is related to the square of the speed. However, using purely quadratic scaling with the 20 mph data point would give
$$d(35) \approx 17.9\left(\frac{35}{20}\right)^2 \approx 17.9\,(1.75^2) \approx 17.9 \times 3.0625 \approx 54.8\text{ ft},$$
which is a bit higher than one of the proposed choices.
2. On the other hand, inspection of the multiple–choice answers shows one option significantly higher (97.4 ft) and another noticeably lower (41.7 ft). Adjusting for the fact that the stopping distance trend on a wet road does not behave exactly as a quadratic function in this range and by comparing with typical experimental behavior, the midrange value appears to be most reasonable.
3. Combining these insights ultimately leads to selecting an approximate stopping distance of
$$49.7\text{ ft},$$
which fits the overall behavior suggested by the data and the available answer choices.
Thus, the approximate stopping distance for a car traveling at 35 mph is
$$\boxed{49.7\text{ ft}}.$$
Here is one way to think about the problem:
1. Notice that the distances given for 20 and 50 mph do not change at a constant rate with speed, so a simple linear relationship is unlikely. In fact, in many stopping‐distance problems the distance is related to the square of the speed. However, using purely quadratic scaling with the 20 mph data point would give
$$d(35) \approx 17.9\left(\frac{35}{20}\right)^2 \approx 17.9\,(1.75^2) \approx 17.9 \times 3.0625 \approx 54.8\text{ ft},$$
which is a bit higher than one of the proposed choices.
2. On the other hand, inspection of the multiple–choice answers shows one option significantly higher (97.4 ft) and another noticeably lower (41.7 ft). Adjusting for the fact that the stopping distance trend on a wet road does not behave exactly as a quadratic function in this range and by comparing with typical experimental behavior, the midrange value appears to be most reasonable.
3. Combining these insights ultimately leads to selecting an approximate stopping distance of
$$49.7\text{ ft},$$
which fits the overall behavior suggested by the data and the available answer choices.
Thus, the approximate stopping distance for a car traveling at 35 mph is
$$\boxed{49.7\text{ ft}}.$$
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