(a) A bumblebee flies with a ground speed of 15.2 m / s. Calculate its speed in km / hr. (b) Th

step 1 we're being asked to do a series of dimensional analysis problems. In part A, we're being asked

(a) A bumblebee flies with a ground speed of 15.2 m / s....

(a) A bumblebee flies with a ground speed of $15.2 \mathrm{~m} / \mathrm{s}$. Calculate its speed in $\mathrm{km} / \mathrm{hr}$. (b) The lung capacity of the blue whale is $5.0 \times 10^{3} \mathrm{~L}$. Convert this volume into gallons. (c) The Statue of Liberty is $151 \mathrm{ft}$ tall. Calculate its height in meters. (d) Bamboo can grow up to $60.0 \mathrm{~cm} /$ day, Convert this growth rate into inches per hour.

(a) A bumblebee flies with a ground speed of $15.2 \mathrm{~m} / \mathrm{s}$. Calculate its speed in $\mathrm{km} / \mathrm{hr}$. (b) The lung capacity of the blue whale is $5.0 \times 10^{3} \mathrm{~L}$. Convert this volume into gallons.
(c) The Statue of Liberty is $151 \mathrm{ft}$ tall. Calculate its height in meters. (d) Bamboo can grow up to $60.0 \mathrm{~cm} /$ day, Convert this growth rate into inches per hour.

Key Concepts

Unit Conversion

Unit conversion is a technique used to change one unit of measurement to another, ensuring that the physical magnitude remains the same. This process involves multiplying by appropriate conversion factors that equate the value of one unit to another and is fundamental in science and everyday applications where measurements need to be expressed in different systems.

Dimensional Analysis

Dimensional analysis is a systematic approach to solving conversion problems by using conversion factors as fractions that cancel out unwanted units. It helps verify that calculations are consistent by ensuring that the final answer has the correct units, making it a valuable tool for converting units in physics, chemistry, and engineering.

Conversion Factors

Conversion factors are numerical ratios that express the equivalence between different units of measurement. They serve as the bridge in unit conversion by providing the relationship between units, such as the relationship between meters and kilometers or liters and gallons, enabling accurate and consistent conversion across different measurement systems.

Metric to Imperial Conversions

Metric to imperial conversions involve translating measurements from the metric system (which is based on powers of ten) to the imperial system (which uses units like feet, inches, and gallons), or vice versa. This is important in contexts where both systems are in use and requires careful application of the appropriate conversion factor for accurate results.

Transcript

00:01 We're being asked to do a series of dimensional analysis problems.

00:03 In part a, we're being asked to convert from meters per second to kilometers per hour.

00:08 We're going to need to look up a conversion factor at some point, but let's set up our problem first.

00:14 So 1, 5 .2, 15 .2 meters.

00:18 When you do dimensional analysis problems, it's important to remember that which unit goes on the bottom and which goes on the top, right? meters are on the top here, seconds are on the bottom, meters per second, okay? and we ultimately want to get to kilometers per hour.

00:37 So this is going to involve a conversion where we convert meters, a measure of distance to kilometer, and seconds to hours.

00:46 So we're going to need the conversion factors for that.

00:49 We can actually start by doing seconds to hours.

00:52 So we know that in every 60 seconds, there is one minute, right? and every 60 minutes is considered one hour, okay? and now if we look, we cancel out seconds, right, by the rules of division, right? seconds on top cancels out with seconds on bottom.

01:13 Minutes on top over here divided by minutes on bottom, and we're left with hours, all right? and so when you work this out, you would just take 15 .2 times 60 times another 60, okay? but before we do that, we have to figure out how i'm going to go from meters to kilometers.

01:36 So it turns out that every 1 ,000 meters is one kilometer.

01:42 So once again, we've canceled out meters, and we're left with kilometers per hour...

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