(12 points, suggested time 25 minutes) Planet I Point C is located at the center of a vertical line between Planet 1 and Planet 2, each of mass M and distance b from point C. Point P lies on the dashed line and is the same distance from the center of Planet 1 and Planet 2. If a spaceship (mass = ms] moves along the dashed line while recording the net b gravitational force Fgras exerted on it by the two planets and measures the greatest Fgra Planet 2 at point P. Note: Figure not drawn to scale. (a) On the dot shown below, draw an arrow which shows the direction of the net gravitational force For when the spaceship is at point P. The arrow should start on the dot! (b) i. For decreases as the spaceship moves to the right from point P (and away from point C). Briefly explain why this happens without deriving equations.Il. Fgray decreases as the spaceship moves to the leftt from point P (and towards from point Briefly explain why this happens without deriving equations. (c) When the ship is on the dashed line a distance x from point C as shown on the Planet 1 (2.G.M.mS ) . 2+ BE right, Fgrav = (x2+62 Ship Derive this equation. The AP definition for derive is; students need to begin their solutions with one or more fundamental equations, such as those given on the AP Physics Exam equation sheet. The final b answer, usually algebraic, is then obtained through the appropriate use of mathematics. Planet 2id) Which term in the Form equation explains why Few decreases as the ship travels to the left from point P towards point C from part (b) ii? X x2+ b2 Explain your answer. (e) The spaceship is at rest at point P when a powerful thruster ignites for a short Planet 1 period of time pushing the spaceship along the dashed line toward point P. After the thruster turn off, the spaceship keeps moving toward point P and just barely makes it to point P. L. The spaceship and the two planets make up the system. Sketch the total mechanical energy E of the system as a function of time from the instant the thruster turns off at Planet 2 time : = 0 until the ship reaches point P at Note: Figure not drawn to scale.ii. If the system is only the ship, does the total mechanical energy of the system increase, decrease, or stay the same from the time the thruster turns off at time t = 0 until the ship reaches point Pat ( = (p Increase Decrease Stay the same Briefly explain your reasoning