. A rocketship of mass mR = 2000 kg tows an asteroid full of valuable minerals with a mass mA = 500 kg with a rope (space rope, or something). The two are out in the far reaches of space, so the gravitational force from the Earth and other planets can be ignored. The asteroid is under the influence of the force of tension from the rope. The rocket is also under the influence of the rope’s force, and it’s also being thrust forward by the force of its engine. The rocket and asteroid both have an acceleration of 0.5 m/s2 (a) What is the strength of the force of the tension in the rope?  (b) What is the strength of the engine’s force on the rocket, and in which direction does it point?

3. A Saturn 5 rocket has a mass of 2,800,000 kg, but can produce 35 million Newtons of force for 3 minutes (180s).  (Spoiler alert: Most of these 35 Mega-Newtons are used to overcome the 28 Mega-Newtons of weight in a concept called “thrust-to-weight ratio”, which means the effective net force on the rocket is only 7,000,000 N.  Use this force, NOT the overall.)   A. Using calculations of either impulse OR kinematics OR both, what is the momentum of the Saturn V rocket after it completes its burn (assuming it starts from rest?   B. Using calculations of either impulse OR kinematics OR both, what is the velocity of the Saturn V rocket after it completes its burn?   C. Once in orbit, if we wanted to slow the rocket down to a specific velocity, describe two methods to do so: one using a single massive object (like a booster stage), the other using compressed nitrogen onboard the rocket.  Make sure you describe the direction and ve

2. A person of mass 60 kg is able to exert a constant 1200 N of force downward when executing a jump by pressing against the ground for t = 0.5 s. (a) Draw freebody diagrams for the person during the moments before the jump, executing the jump, and right after taking off. (b) How long would they be airborne on the moon, which has gravita- tional acceleration of moon 1.62 m/s²? =

9. A 770 kg car, with a 95 kg driver, is driving up a shallow hill of angle 0=5° directly into a strong headwind. The headwind exerts a force 200 N on the car. The coefficient of rolling friction for the car on the road is 0.025. What force must the car's engine produce so that it travels at a constant velocity of 10 m/s.