A speed boat has a top speed of 46 knots (nautical miles per hour). What is this speed in miles

A speed boat has a top speed of 46 knots (nautical miles per...

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Key Concepts

Dimensional Analysis

Dimensional analysis is a method used to check the consistency of equations and computations involving physical quantities. By ensuring that the dimensions on both sides of an equation match, this technique facilitates the correct application of conversion factors and prevents errors in calculations.

Nautical Mile

A nautical mile is a unit of distance used primarily in maritime and aviation contexts. It is based on the circumference of the Earth and differs from a statute mile, which is commonly used on land. Understanding the relationship between these units is key when converting speeds measured in knots (nautical miles per hour) to miles per hour.

Unit Conversion

This refers to the process of converting a quantity expressed in one set of units to another set of units. Understanding unit conversion is essential in many fields such as physics, engineering, and everyday problem-solving where measurements need to be expressed in different systems for clarity or standardization.

Conversion Factor

A conversion factor is a numerical multiplier that relates two units of measurement. In unit conversion problems, it is used to transform measurements from one unit to another while preserving the same physical quantity. This concept is crucial when working with units that are not part of the same measurement system.

Transcript

00:01 In this problem, this is sort of a fun problem, we are given some information.

00:07 One nautical mile is equal to 6 ,076 .12 feet.

00:21 And we're also given that one knot is equal to one nautical mile, which i'm going to abbreviate nm per hour.

00:36 I better write a nicer hr because nobody can read my hr.

00:41 H .r.

00:42 There we go.

00:42 That's for our.

00:44 For the first part of what we're working on, we are asked to, i'll call this a, um, one nautical mile equals how many actual miles? in order to do this, we have how many feet one nautical mile.

01:09 We know one nautical mile equals 6 ,076 .12 feet.

01:19 Um, so i'm just going to start with and i also know that one mile is equal to 5 ,280 feet.

01:33 So we'll start with 6 ,076 .12 feet, which is a nautical mile and we're going to multiply that by this equality 5 ,280 feet equals one mile.

01:49 I'll switch colors so you can see what's crossing off.

01:52 Do my math and we get 1 .15 078 miles.

02:03 I kept six significant figures here because this equality had six significant figures.

02:14 For the second part of this problem, we are asked how many meters this is.

02:20 A equals how many meters? that's our unknown.

02:27 There's a couple things i'm just going to outline these as i do this...

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