This problem has two parts to it. I will be typing the questions for both parts and other info in "Description"

Question

When the moon is directly overhead at sunset, the gravitational force on the Moon due to Earth, F_EM, is perpendicular to the gravitational force on the Moon due to the Sun, F_SM. These two forces have magnitudes F_EM = 1.98 × 10²⁰ N and F_SM = 4.36 × 10²⁰ N. Assume that all other forces are negligible. The mass of the Moon is m = 7.35 × 10²² kg.

Part a) Write an expression for the magnitude of the acceleration of the Moon.

Part b) What is the acceleration of the Moon in m/s²?

Answer 1

An unbalanced force will cause an acceleration according to Newton's second law:

Net force = mass * acceleration

Each of the two gravitational forces (from the Earth and from the Sun) that act on the Moon therefore each cause some acceleration of the moon. We can find the magnitude of each of those components of acceleration by dividing each force by the mass of the moon.

After doing so, the two components of acceleration will need to be combined. As they are perpendicular to each other, we have to add them using the Pythagorean theorem. Essentially, the two components make the two legs of a right triangle, and the overall magnitude will be the length of the hypotenuse of that right triangle.