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Chapter 6: Problem 80

A car moving at \(30 \mathrm{mi} / \mathrm{h}\) is stopped by jamming on the brakes and locking the wheels. The car skids 50 ft before coming to rest. How far would the car skid if it were initially moving at $60 \mathrm{mi} / \mathrm{h} ?$ [Hint: You will not have to do any unit conversions if you set up the problem as a proportion. \(]\)

Short Answer

Expert verified
Answer: The car would skid 200 ft if its initial speed was doubled.

Step by step solution

01

Set up the proportion

Since the car's initial speed is related to the distance it skids, we can set up a proportion to relate the two situations. Let \(d_1\) be the distance the car skids when moving at \(30 \mathrm{mi} / \mathrm{h}\), and \(d_2\) be the distance it skids when moving at \(60 \mathrm{mi} / \mathrm{h}\). Then, we can write the proportion as: $$ \frac{d_1}{30^2} = \frac{d_2}{60^2} $$
02

Plug in given values

We are given that the car skids 50 ft when its initial speed is \(30 \mathrm{mi} / \mathrm{h}\). Using this information, we can replace \(d_1\) with the given value in our proportion: $$ \frac{50}{30^2} = \frac{d_2}{60^2} $$
03

Solve for the unknown distance \(d_2\)

To find \(d_2\), we can cross-multiply and solve: $$ 50 \cdot 60^2 = 30^2 \cdot d_2 $$ Now, simplify and solve for \(d_2\): $$ d_2=\frac{50 \cdot 60^2}{30^2} $$ $$ d_2 = \frac{50 \cdot 3600}{900} $$ $$ d_2 = 200 $$
04

Interpret the result

The car would skid 200 ft if it were initially moving at \(60 \mathrm{mi} / \mathrm{h}\).

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