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Chapter 1: Problem 54

The world record for the hundred meter dash is 9.58 s. What is the corresponding average speed in units of $\mathrm{m} / \mathrm{s}, \mathrm{km} / \mathrm{h}\( , \)\mathrm{ft} / \mathrm{s}$ , and mi/h? At this speed, how long would it take to run \(1.00 \times\) \(10^{2}\) yards?

Short Answer

Expert verified
The average speed for the 100-meter dash world record is approximately 10.44 m/s, 37.60 km/h, 34.24 ft/s, and 23.35 mi/h. At this speed, it would take about 8.76 seconds to run 100 yards.

Step by step solution

01

Convert the distance to different units

First, let's convert 100 meters to other units so we can later calculate the average speed. 1 meter = 3.28084 feet 1 meter = 0.001 km So, 100 meters is equal to: - 100 * 3.28084 ft = 328.084 ft - 100 * 0.001 km = 0.1 km
02

Calculate the average speed in different units

Now, we will use the Speed formula to find the average speed in different units: - m/s: Speed = 100 m / 9.58 s = 10.44 m/s - km/h: Speed = 0.1 km / (9.58 / 3600) h = 37.60 km/h (rounding to 2 decimal places) - ft/s: Speed = 328.084 ft / 9.58 s = 34.24 ft/s (rounding to 2 decimal places) To convert ft/s to mi/h, we need to use the following conversion factor: 1 ft/s = 0.681818 mi/h - mi/h: Speed = 34.24 ft/s * 0.681818 mi/h = 23.35 mi/h (rounding to 2 decimal places)
03

Convert 100 yards to meters

Before calculating the time it would take to run 100 yards, we need to convert it to meters: 1 yard = 0.9144 m 100 yards = 100 * 0.9144 m = 91.44 m
04

Calculate the time to run 100 yards

Now we will use the time formula to find the time it would take to run 100 yards. We will use the speed in m/s that we calculated earlier: Time = Distance / Speed Time = 91.44 m / 10.44 m/s = 8.76 s (rounding to 2 decimal places) So, at the world record speed, it would take approximately 8.76 seconds to run 100 yards.

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