Answer :
We start with the given radius of the Moon, which is
[tex]$$
r = 1,\!740,\!000 \text{ m}.
$$[/tex]
Step 1. Calculate the Circumference
The circumference of a circle is given by
[tex]$$
C = 2\pi r.
$$[/tex]
Substituting the given value of [tex]$r$[/tex], we get
[tex]$$
C = 2\pi \times 1,\!740,\!000 \approx 10,\!932,\!742.43 \text{ m}.
$$[/tex]
Step 2. Verify the Speed Requirement
It is stated that the football needs to travel at a speed of
[tex]$$
v = 1680 \text{ m/s}.
$$[/tex]
Step 3. Find the Time for One Complete Circumnavigation
Time is obtained by dividing the total distance (circumference) by the speed:
[tex]$$
t = \frac{C}{v}.
$$[/tex]
Substitute the known values:
[tex]$$
t = \frac{10,\!932,\!742.43 \text{ m}}{1680 \text{ m/s}} \approx 6507.58 \text{ s}.
$$[/tex]
Final Answers:
a) The speed required is
[tex]$$
1680 \text{ m/s}.
$$[/tex]
b) The time required to go around the Moon once is approximately
[tex]$$
6507.58 \text{ s}.
$$[/tex]
[tex]$$
r = 1,\!740,\!000 \text{ m}.
$$[/tex]
Step 1. Calculate the Circumference
The circumference of a circle is given by
[tex]$$
C = 2\pi r.
$$[/tex]
Substituting the given value of [tex]$r$[/tex], we get
[tex]$$
C = 2\pi \times 1,\!740,\!000 \approx 10,\!932,\!742.43 \text{ m}.
$$[/tex]
Step 2. Verify the Speed Requirement
It is stated that the football needs to travel at a speed of
[tex]$$
v = 1680 \text{ m/s}.
$$[/tex]
Step 3. Find the Time for One Complete Circumnavigation
Time is obtained by dividing the total distance (circumference) by the speed:
[tex]$$
t = \frac{C}{v}.
$$[/tex]
Substitute the known values:
[tex]$$
t = \frac{10,\!932,\!742.43 \text{ m}}{1680 \text{ m/s}} \approx 6507.58 \text{ s}.
$$[/tex]
Final Answers:
a) The speed required is
[tex]$$
1680 \text{ m/s}.
$$[/tex]
b) The time required to go around the Moon once is approximately
[tex]$$
6507.58 \text{ s}.
$$[/tex]
