Final answer:
Formula B (v^2 = G) should be used to calculate the tangential speed of both the moon and a satellite in their respective orbits around Earth, applying Newton's law of universal gravitation and the principles of circular motion.
Step-by-step explanation:
To determine the tangential speed of the moon, given the mass of Earth and the distance from Earth to the moon, you would use formula B (v^2 = G), which relates the orbital velocity to the gravitational constant and the mass and radius of the celestial bodies in question. This formula is derived from Newton's law of universal gravitation and the formula for centripetal acceleration, which applies because the moon's path around Earth is nearly circular.
For the second scenario, finding the tangential speed of a satellite that takes 90 minutes to orbit 150 km above Earth's surface, you would also use formula B (v^2 = G). You have the period of the orbit (90 minutes), and by adding the altitude above Earth's surface to Earth's radius, you can calculate the radius of the satellite's orbit. You can use this along with the gravitational constant and Earth's mass to determine the satellite's orbital velocity.