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Chapter 1: Problem 19

Solve the following problem and express the answer in meters per second \((\mathrm{m} / \mathrm{s})\) with the appropriate number of significant figures. \((3.21 \mathrm{m}) /(7.00 \mathrm{ms})=?\) [Hint: Note that ms stands for milliseconds.]

Short Answer

Expert verified
Express your answer with the correct number of significant figures. Answer: The speed of the sprinter is 459 m/s.

Step by step solution

01

Convert Units

First, we need to convert the time from milliseconds to seconds. To do this, we can use the fact that there are 1000 milliseconds in 1 second: \((7.00 \mathrm{ms}) \times (1\, \mathrm{s}/1000\, \mathrm{ms}) = 0.00700\, \mathrm{s}\).
02

Calculate Speed

Now we can compute the speed using the formula: \(speed = distance/time\). Plugging in the given values, we get: \(speed = (3.21 \mathrm{m}) / (0.00700 \mathrm{s})\).
03

Divide And Apply Significant Figures

Next, divide the distance by the time to find the speed: \(3.21/0.00700 = 458.57\). Since the input values have 3 significant figures each, the final answer should also have 3 significant figures: \(speed = 459\, \mathrm{m/s}\).

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Most popular questions from this chapter

How many significant figures are in each of these measurements? (a) \(7.68 \mathrm{g}\) (b) \(0.420 \mathrm{kg}\) (c) \(0.073 \mathrm{m}\) (d) \(7.68 \times 10^{5} \mathrm{g}\) (e) \(4.20 \times 10^{3} \mathrm{kg}\) (f) \(7.3 \times 10^{-2} \mathrm{m}\) (g) \(2.300 \times 10^{4} \mathrm{s}\)
It is useful to know when a small number is negligible. Perform the following computations. (a) \(186.300+\) 0.0030 (b) \(186.300-0.0030\) (c) $186.300 \times 0.0030\( (d) \)186.300 / 0.0030$ (e) For cases (a) and (b), what percent error will result if you ignore the \(0.0030 ?\) Explain why you can never ignore the smaller number, \(0.0030,\) for case (c) and case (d)? (f) What rule can you make about ignoring small values?

A sheet of paper has length \(27.95 \mathrm{cm},\) width 8.5 in., and thickness \(0.10 \mathrm{mm} .\) What is the volume of a sheet of paper in \(\mathrm{m}^{3} ?\) (Volume \(=\) length \(\times\) width \(\times\) thickness.)
Perform these operations with the appropriate number of significant figures. (a) \(3.783 \times 10^{6} \mathrm{kg}+1.25 \times 10^{8} \mathrm{kg}\) (b) $\left(3.783 \times 10^{6} \mathrm{m}\right) \div\left(3.0 \times 10^{-2} \mathrm{s}\right)$
Convert \(1.00 \mathrm{km} / \mathrm{h}\) to meters per second $(\mathrm{m} / \mathrm{s})$
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