Answer
The velocity of a satellite in geosynchronous orbit about the earth:
$v \simeq 3071.85$ m/s
Work Step by Step
Since the satellite is a geosynchronous orbit about the earth, we can use the results from Exercise 6 and 9.
Using the result in Exercise 6, the radius of the orbit is $R \approx 42246$ km.
Now, the velocity of the satellite using result in Exercise 9 is
$v = \sqrt {\frac{k}{R}} = \sqrt {\frac{{GM}}{R}} $, ${\ \ \ }$ where $k = GM$.
$G$ is the gravitational constant: $G \simeq 6.673 \times {10^{ - 11}}$ ${m^3}k{g^{ - 1}}{s^{ - 2}}$ and $M$ is the mass of the earth: $M \approx 5.974 \times {10^{24}}$ kg.
Substituting $G$, $M$, and $R$ in $v$ gives the velocity of a satellite in geosynchronous orbit about the earth:
$v = \sqrt {\frac{{6.673 \times {{10}^{ - 11}} \times 5.974 \times {{10}^{24}}}}{{42.246 \times {{10}^6}}}} \simeq 3071.85$ m/s
