3. A satellite is launched from the surface of the earth at the initial speed of 8 km/s. How high will it go before it stops and starts falling back to the earth?

Spaceship Malfunction. You and your team get a distress call from another ship indicating that there has been an explosion and their propulsion and navigation systems are now off line. A large piece of their ship has been jettisoned into space, and their life support systems are failing. They need help as soon as possible. You try to track them, but are only able to pick up the piece of the craft that had been projected away from them in the explosion. You look up the make and model of their ship, a Galaxy Explorer 5000 (GE 5000), which has a total mass of 51000 kg. The piece heading in your direction is the ship's storage module, and has a mass of 8500 kg. The GE 5000 was at rest with respect to your ship at the time of the explosion. (a) Assuming you received the distress call 20 minutes before the jettisoned storage module passed by your ship at a speed of 650 m/s, what is the speed of the damaged craft? (b) How far away is the Galaxy Explorer 5000 when its storage module passes by?…

3. A 1-kg mass at sea level on Earth (g = 9.80 m/s²) weighs 2.2 lbs. How much would a baseball (m = 145 g) weigh on Earth? On the moon (g 1.62 m/s²)? On the sun (g = 274 m/s²)? On Mars (g = 3.71 m/s²)? On Jupiter (g 24.8 m/s²)? (1 N = 0.22 lbs) =

On planet #3, you fire a projectile horizontally from the edge of a vertical cliff 76.0 m above the ground, with an initial speed of 31.2 m/s. The projectile lands 71.5 m away from the base of the cliff. What is the value of g for planet #3?     848.50 m/s^2     28.94 m/s^2     14.47 m/s^2     12.05 m/s^2

Two planets of equal mass orbit a much more massive star. Planet m 1 moves in a circular orbit of radius r 1 = 10^11 m with a period of 2 years (= 6.3 x 10^7 s). Planet m 2 moves in an elliptical orbit with its closes t distance r 1 and its farthest distance r 2 = 1.8 x 10^11 m. a. Find the period of m 2’s orbit. b. The elliptical orbit has greater energy. Which planet has the greater potential energy at point P? Justify. c. Which planet has the greater speed at point P? Justify. d. How does the speed of m 2 at point P compare with the speed at point A? Justify.

13. A skier/snowboarder starts at rest at the top of a snowy (friction-free) hill with height h₁. After the bottom of this hill there is a small "jump" hill. The top of the jump has height h, and a curvature of radius R. What is the minimum height of the starting hill, himin, so that the skier/snowboarder jumps or "catches air" at the top of hill 2? Solve for himin in terms of h₂, R, and g. Hint: if the skier/snowboarder jumps, he/she/they loose contact with the snowy ground. h₁ to jump!

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1. On a planet whose radius is 1.5 × 107 m, the acceleration due to gravity is 20 m/s². An astronaut with a mass of 60 kg is standing on its surface.

1. What is the gravitational potential energy in a system of three objects with masses m₁ = 2.0 × 1020 kg, m2 = 4.0 × 1020 kg, and m3 1.0 × 1021 located at r₁ = 2.0 × 10¹3 m 1.0 × 106 m -1.3 × 10¹2 m 1 respectively? 9 r2 = -6.0 × 10¹3 m 2.2 × 10¹² m –5.7 × 10³ m {] 9 T3 = = 1.5 × 10¹1 m −6.5 × 10² m 9.2 × 10¹0 m

Some of the most spectacular objects in the universe are fairly small: neutron stars are spheres with a diameter that's about 10km (they are remnants of old stars). Their spectacular nature is indicated by the fact that they are about as massive as the sun, i.e. 2 x 1030kg. What is the gravitational acceleration on the surface of such an object? Express your result as a multiple of g.