/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 2 Vesna Vulovic survived the longe... [FREE SOLUTION] | 91Ó°ÊÓ

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Vesna Vulovic survived the longest fall on record without a parachute when her plane exploded and she fell 6 miles, 551 yards. What is this distance in meters?

Short Answer

Expert verified
The distance in meters is approximately 10159 meters.

Step by step solution

01

Convert Miles to Yards

The first step is to convert the distance Vesna fell from miles to yards. There are 1760 yards in one mile. Thus, you multiply 6 miles by 1760 yards per mile to find the number of yards: \[ 6 \text{ miles} \times 1760 \frac{\text{yards}}{\text{mile}} = 10560 \text{ yards} \]
02

Add Additional Yards

The distance also includes an additional 551 yards. We need to add this to the previously calculated distance in yards (10560 yards from 6 miles):\[ 10560 \text{ yards} + 551 \text{ yards} = 11111 \text{ yards} \]
03

Convert Yards to Meters

Next, convert the total distance from yards to meters. There are approximately 0.9144 meters in one yard. Use this conversion factor to convert 11111 yards to meters:\[ 11111 \text{ yards} \times 0.9144 \frac{\text{meters}}{\text{yard}} = 10158.8184 \text{ meters} \]
04

Round to Nearest Meter

Finally, round the calculated result to the nearest whole number to express the distance in meters as simply as possible.\[ 10158.8184 \text{ meters} \approx 10159 \text{ meters} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Distance Measurement
Distance measurement is a fundamental concept in both everyday life and scientific research. When we talk about measuring distance, we're referring to determining how far apart two points are. Distance can be measured in various units, depending on the system of measurement being used. For instance, in the Imperial system, common units include miles, yards, and inches, while in the Metric system, meters, kilometers, and centimeters are typically used. Accurate distance measurements are crucial for tasks ranging from land surveying to sports and aviation. In this exercise, calculating the distance of Vesna Vulovic's fall required converting her fall's measurement from miles and yards into a more universally understood unit—meters. This conversion provides a clearer understanding of the distance, as the metric system is used worldwide.
Metric System
The Metric system is a decimal-based system of measurement used around the world. It was developed to simplify the process of measurement by providing a standard that's easy to understand and use. The Metric system uses units like meters for measuring distance, liters for volume, and grams for weight, all derived from base units of ten. Everything in the Metric system is scalable and relates uniformly with other units. This makes the Metric system particularly convenient when converting between units. For example, 1 kilometer is 1000 meters and 1 meter is 100 centimeters. This consistency helps avoid complex conversions and reduces errors. Given the calculation in the exercise, converting yards to meters utilizes a common factor. It makes the communication and comprehension of data between different regions of the world much more efficient. This is why it's often preferred in scientific and technical fields, where precision and standardization are crucial.
Conversion Factors
Conversion factors are necessary tools that allow us to switch between units of measurement seamlessly. They represent the relationship between two different units, serving as a bridge to translate one measurement into another. For instance, to convert from miles to yards, we use the conversion factor that 1 mile is equivalent to 1760 yards. Similarly, to convert from yards to meters, we use 1 yard equals approximately 0.9144 meters. These factors are key to ensuring accuracy when converting, enabling us to perform calculations that maintain the integrity of measurements. In the example of Vesna's fall, using these factors allowed us to systematically convert from miles and yards directly to meters. Always remember, when performing conversions, to multiply by the appropriate conversion factor to switch seamlessly from one unit to another. Conversion factors play a crucial role in various fields, from engineering to cooking, where precise measurement is required for success.

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Most popular questions from this chapter

A circus performer begins his act by walking out along a nearly horizontal high wire. He slips and falls to the safety net, \(25.0 \mathrm{ft}\) below. The magnitude of his displacement from the beginning of the walk to the net is \(26.7 \mathrm{ft}\). (a) How far out along the high wire did he walk? (b) Find the angle that his displacement vector makes below the horizontal.

Your friend has slipped and fallen. To help her up, you pull with a force \(\overrightarrow{\mathbf{F}},\) as the rawing shows. The vertical component of this force is 130 newtons, and the horizontal omponent is 150 newtons. Find (a) the magnitude of \(\overrightarrow{\mathbf{F}}\) and (b) the angle \(\theta\).

The mass of the parasitic wasp Caraphractus cintus can be as small as \(5 \times 10^{-6} \mathrm{~kg}\). What is this mass in (a) grams (g), (b) milligrams (mg), and (c) micrograms\((\mu g) ?\)

Consider the following four force vectors: $$ \begin{array}{l} \overrightarrow{\mathbf{F}}_{1}=50.0 \text { newtons, due east } \\\ \overrightarrow{\mathbf{F}_{2}}=10.0 \text { newtons, due east } \\\ \overrightarrow{\mathbf{F}_{3}}=40.0 \text { newtons, due west } \\\ \overrightarrow{\mathbf{F}}_{4}=30.0 \text { newtons, due west } \end{array} $$ Which two vectors add together to give a resultant with the smallest magnitude, and which two vectors add to give a resultant with the largest magnitude? In each case specify the magnitude and direction of the resultant.

A spring is hanging down from the ceiling, and an object of mass \(m\) is attached to the free end. The object is pulled down, thereby stretching the spring, and then released. The object oscillates up and down, and the time \(T\) required for one complete up-and-down oscillation is given by the equation \(T=2 \pi \sqrt{m / k},\) where \(k\) is known as the spring constant. What must be the dimension of \(k\) for this equation to be dimensionally correct?

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