Chapter 4.2, Problem 49E

(a)

To determine

To Analyze: The greatest number of minutes that could be in a space hour.

Answer to Problem 49E

25 hours

Explanation of Solution

Given: In the future, scientists may want to make a unit of time that is convenient for people living on both Earth and Mars. The new unit of time, called the space-hour, should divide evenly into the number of minutes in each planet’s day. Under the current Earth definition of minutes, Earth has 1440 minutes per day, and mars has approximately 1480 minutes per day.

In one hour is 60 minutes.

For Earth

So, Time in space-hour $\frac{1440}{60}=24\text{ hours }$

For Mars

So, Time in space-hour $\frac{1480}{60}=24.67\approx 25\text{ hours }$

On mars number of minutes in space-hour is greater than Earth.

(b)

To determine

To Find: The space-hours on Earth and Mars.

Answer to Problem 49E

Earth $=24\text{ hours }$

Mars $=25\text{ hours }$

Explanation of Solution

Given: In the future, scientists may want to make a unit of time that is convenient for people living on both Earth and Mars. The new unit of time, called the space-hour, should divide evenly into the number of minutes in each planet’s day. Under the current Earth definition of minutes, Earth has 1440 minutes per day, and mars has approximately 1480 minutes per day.

In one hour is 60 minutes.

For Earth

So, Time in space-hour $\frac{1440}{60}=24\text{ hours }$

For Mars

So, Time in space-hour $\frac{1480}{60}=24.67\text{ hours }$

(C)

To determine

To find: The time travels from Earth to Mars.

Answer to Problem 49E

5145 hours

Explanation of Solution

Given: In the future, scientists may want to make a unit of time that is convenient for people living on both Earth and Mars. The new unit of time, called the space-hour, should divide evenly into the number of minutes in each planet’s day. Under the current Earth definition of minutes, Earth has 1440 minutes per day, and mars has approximately 1480 minutes per day.

A spacecraft that uses current technology can take 210 days to travel from Earth to Mars.

First find the mean of space-hours of both Earth and Mars.

The average of space-hour is 24.5 hour per day.

Total time to travel from Earth to Mars in 210 days.

Now convert into space-hours

In 1 day space−hour = 24.5 hours

In 210 days space-hours $=24.5\times 210=5145\text{ hours}$