In the final stages of a moon landing, the lunar module descends under retrothrust of its descent engine to within h = 5.2 m of the lunar surface where it has a downward velocity of 2.8 m/s. If the descent engine is cut off abruptly at this point, compute the impact velocity v of the landing gear with the moon. Lunar gravity is 1/6 of the earth's gravity. Answer: v= i 4.122 m/s

Consider a Falcon 9, a two-state-to-orbit launch vehicle. The take-off mass of Falcon 9 is Mto = 550,000 kg, the first stage fuel burn rate is m = 2500 kg/s over a maximum of 160 s, and constant thrust of T = 7500 kN. Making a lot of simplifying assumptions including constant gravity, no aerodynamic drag, thrust constant with altitude, we can approximate the vertical acceleration as: T-mog+mgt mo -mt Calculate the altitude (in km) at t = 135 s. ay (t)

Weight w are fired from a giant cannon made by a shooting club. In early tests of the cannon, pointed straight up, the people want to shoot a projectile to an altitude of 1.5RE, where RE is the radius of the earth. Dismiss the effects of air resistance and the rotation of the earth.  (Note: g  = GME/RE2, where G is Newton’s gravitational constant, ME is the mass of the earth and RE is the radius of the earth.) What must the muzzle speed of the projectile be for it to get this high? What is the speed of the projectile when it returns to the surface of the earth (just before hitting the ground)?

Apollo 14 astronaut Alan B. Shepard Jr. used an improvised six-iron to strike two golf balls while on the Fra Mauro region of the moon’s surface, making what some consider the longest golf drive in history. Assume one of the golf balls was struck with initial velocity v0 = 69 m/s at an angle θ = 50° above the horizontal. The gravitational acceleration on the moon’s surface is approximately 1/6 that on the earth’s surface. Use a Cartesian coordinate system with the origin at the ball's initial position.   What horizontal distance, R in meters, did this golf ball travel before returning to the lunar surface?