Final answer:
The speed (v) of the GPS satellite in orbit at an altitude of 2.09x10^4km above the Earth's surface is approximately 3.87 km/s.
Step-by-step explanation:
The speed of a satellite in orbit can be determined using the formula for orbital speed. For a circular orbit, the orbital speed (v) can be calculated using the following formula:
v = GM/r
where:
G is the gravitational constant (6.67430x 10^-11 m^3kg^-1 s^-2),
M is the mass of the Earth (5.972×10^24kg)
r is the radius of the orbit (altitude above the Earth's surface plus the Earth's radius).
Given that the altitude above the Earth's surface is 2.09×10^4km we need to convert this to meters and then use it in the formula.
r=altitude+Earth’s radius
r=(2.09×10^4km+6.371×10^6m)
Once you have r, you can plug the values into the formula to find the orbital speed v. Make sure to use consistent units (meters) for the calculation. The resulting speed will be in meters per second (m/s).