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Chapter 1: Problem 36

The average distance from Earth to the Moon is \(384,400 \mathrm{km}\). In the late 1960 s, astronauts reached the Moon in about 3 days. How fast (on average) must they have been traveling (in kilometers per hour) to cover this distance in this time? Compare this speed to the speed of a jet aircraft \((800 \mathrm{km} / \mathrm{h})\).

Short Answer

Expert verified
The astronauts' average speed was approximately 5,339 km/h, which is about 6.67 times faster than a jet aircraft.

Step by step solution

01

Understand the Problem

To find the average speed of the astronauts, divide the total distance traveled by the total time taken. The distance from Earth to the Moon is given as 384,400 km, and the time taken is 3 days.
02

Convert Time

Convert the time from days to hours because we need the speed in kilometers per hour (km/h). There are 24 hours in a day, so multiply the number of days by 24 to get the time in hours.Time in hours = 3 days * 24 hours/day = 72 hours
03

Apply the Speed Formula

Use the formula for speed, which is distance divided by time.Speed = Distance / Time Speed = 384,400 km / 72 hours
04

Calculate the Speed

Perform the division to find the average speed.Speed = 384,400 / 72 Speed ≈ 5,339 km/h
05

Compare with Jet Aircraft Speed

The speed of a jet aircraft is given as 800 km/h. To compare, divide the astronauts' speed by the jet aircraft's speed.Speed ratio = Astronaut speed / Jet speedSpeed ratio = 5,339 km/h / 800 km/h Speed ratio ≈ 6.67. So, the astronauts were traveling approximately 6.67 times faster than a jet aircraft.

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Key Concepts

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

distance calculation
When calculating the distance an astronaut travels, the first step is to identify the total distance between two points. In this exercise, the task is to find the average travel speed of astronauts traveling from Earth to the Moon, which has an average distance of 384,400 km. It's the first essential piece of information to solve our problem. Once you have the distance, you can move on to other calculations, such as converting units and applying formulas.
speed formula
The speed formula is crucial for solving problems related to motion. The formula is: Speed = Distance / Time. This simple equation means that the speed is calculated by dividing the distance traveled by the time taken to travel that distance. In our problem, the distance is 384,400 km, and the time is 3 days, which we will need to convert into hours to find the speed in km/h. This formula is straightforward and can be used for any linear motion problem.
unit conversion
Unit conversion is an essential step when working with different measurement units in a problem. In this case, we need to find the speed in kilometers per hour (km/h), but the time is given in days. We know that there are 24 hours in a day, so we multiply the number of days by 24 to convert the time into hours. Time in hours = 3 days * 24 hours/day = 72 hours. By converting the time into hours, we can use the speed formula more effectively and get the answer in the desired units.
comparison of speeds
Once we have calculated the speed, we can compare it with other speeds to understand how fast the astronauts were traveling. The equation we use to compare speeds is: Speed ratio = Astronaut speed / Jet speed. Given that a typical jet aircraft travels at 800 km/h, we divide the astronaut speed by 800 km/h to get the ratio. For instance, if the astronaut speed is approximately 5,339 km/h, we get Speed ratio ≈ 6.67. This means the astronauts were traveling roughly 6.67 times faster than a jet aircraft. Such comparisons help illustrate the vast differences in speed between space travel and conventional air travel.

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