Question $1(4$ points$)$:

Purpose: To practice recursion with a simple example.

Moosetopia$$s most famous rocket scientist, Zeno, has invented a new kind of space ship which will enable

interstellar travel across the large distances of space very quickly. The technology is very complicated, and

involves a lot of tedious messing about in hyperspace, but the actual motion of the ship is quite simple:

$$ If the distance to the destination is greater than $1$ meter, the ship will "fold space" and "jump" to a

position half way to the destination. It takes exactly one minute for the ship$$s computer to do the

calculations prior to the jump. The jump itself is instantaneous.

$$ Any distance of $1$ meter or less will take exactly one minute, using normal impulse rockets.

For example, if the ship has to travel $10$ meters, it will jump $5$ meters after the first minute, $2\mathrm{.}5$ meters the

second minute, $1\mathrm{.}25$ meters the $3$rd minute, and $0\mathrm{.}625$ meters the fourth minute. Finally, the remaining

$0\mathrm{.}625$ meters takes one more minute. Thus the total time to travel $10$ meters is $5$ minutes. $($That seems

very slow, and it is for small distances; the true value of this method only reveals itself for large distances.$)$

Write a recursive function called spaceTime$()$ that calculates the time needed for Zeno$$s ship to travel a

given distance. In the same file, write a program that asks the user for a distance in meters $($console input$)$

then call your spaceTime$()$ function to calculate the time required to travel the given distance.

Test your function out on all of the following examples:

$$ Average distance to the nearest coffee shop: $537$ meters $($about a typical Moosetopia city block$).$

$$ Average distance from Moosetopia to its biggest moon: $3\mathrm{.}84$e$8$ meters $($about $400$ thousand km$).$

$$ Average distance between our earth and our sun: $1\mathrm{.}49$e$11$ meters $($about $150$ million km$).$

$$ Approximate distance between the sun and the closest star: $4\mathrm{.}0$e$16$ meters $($about $4$ light$-$years$).$

$$ Size of the observable universe: $8\mathrm{.}8$e$26$ meters $($about $93$ Giga$-$light$-$years$)$

Sample Run

Your program output might look something like the following:

Zeno $$ s drive requires :

$-11$ minutes to travel $537$ meters to Zeno $$ s nearest coffee shop

$-30$ minutes to travel $384000000\mathrm{.}0$ meters from Moosetopia to its biggest moon

$-39$ minutes to travel $149000000000\mathrm{.}0$ meters from our earth to our sun

$-57$ minutes to travel $4$ e $+16$ meters from our sun to the nearest star

$-91$ minutes to travel $8\mathrm{.}8$ e $+26$ meters across the observable universe

What to Hand In

$$ A d