La distancia entre la Tierra y la Luna es de aproximadamente 240,000 mi. (a) Exprese esta distan

La distancia entre la Tierra y la Luna es de aproximadamente...

La distancia entre la Tierra y la Luna es de aproximadamente $240,000 \mathrm{mi}$. (a) Exprese esta distancia en metros. (b) El Concorde SST tiene una velocidad respecto al aire de $2400 \mathrm{~km} / \mathrm{h}$. Si el Concorde pudiera volar a la Luna, ¿cuántos segundos tardaría?

Key Concepts

Unit Conversion

This concept involves converting measurements from one system of units to another, such as converting miles to meters or kilometers per hour to meters per second. It requires a clear understanding of the conversion factors that relate different units.

Dimensional Analysis

This technique is used to ensure that mathematical equations and computations make sense in terms of units. By carefully handling unit conversion factors, one can convert quantities between measurement systems while maintaining the integrity of the physical quantities.

Distance-Speed-Time Relationship

This basic relationship in kinematics shows that time is equal to distance divided by speed. It is a fundamental concept in physics and engineering, allowing for the calculation of travel time when distance and speed are known.

Conversion of Speed Units

This involves changing the units of speed to maintain consistency in calculations with distance and time. For example, converting kilometers per hour to meters per second involves using factors such as 1 km = 1000 m and 1 hour = 3600 seconds.

Transcript

0:00 Okay.

00:02 In this problem, we are being asked to use different conversion factors in order to convert the number were given the distance from earth to the moon into other quantities.

00:13 The first part of this question, part a asks us what the distance from the earth to the moon is in meters were given that the earth to the moon is 240,000 miles.

00:26 So we're going to start with that in our conversion chart.

00:31 Now we want to put miles on the bottom so that we can cancel out these units.

00:38 And what we want to do now is we want to search up or find or even just pull from your brain.

00:45 The value that converts from miles two m.

00:48 So one mile is equal to 1609 2.34 meters.

00:57 And then all we need to do is just multiply those two values and we get this very large value missed one day.

01:09 Okay.

01:15 We can also, if you are asked convert this value and make sure that it's right based on sig figs.

01:20 So we have 123456 significant figures.

01:24 123456 so with sig figs are value would be that the next part of this question asks us to figure out how many seconds it would take for us to get from the earth to the moon at a rate that were given at the rate of 350 km/s or per hour.

01:57 So we're gonna store that in our back pocket for now.

02:00 And we're going to set up our chart again and start doing what we know how to do because we just did in the last problem, we're going to convert one mile to 1609 point.

02:14 Now the conversion rate for m, two km, 1000 m is equal to one km.

02:23 And then we're gonna insert our rates that were able to cancel out our km because we are looking for our quantity in time in one hour.

02:37 And when we do out this problem, we had a final answer 4.0 times 10 to the sixth seconds.

02:49 In part c.

02:50 We are given the speed of light and were asked how long it takes for light to travel from the earth to the moon and then back.

03:00 So unlike the other two problems, we're not, we're not only going to 240,000 miles, but then we're going another 240,000 back.

03:10 So there are multiple ways to solve this one...

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