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- A team of astronauts is on a mission to land on and explore a large asteroid. In addition to collecting samples and performing experiments, one of their tasks is to demonstrate the concept of the escape speed by throwing rocks straight up at various initial speeds. With what minimum initial speed ?esc will the rocks need to be thrown in order for them never to "fall" back to the asteroid? Assume that the asteroid is approximately spherical, with an average density ?=2.93×106 g/m3 and volume ?=1.94×1012 m3 . Recall that the universal gravitational constant is ?=6.67×10-11 N·m2/kg2 .vesc = ? m/sA team of astronauts is on a mission to land on and explore a large asteroid. In addition to collecting samples and performing experiments, one of their tasks is to demonstrate the concept of the escape speed by throwing rocks straight up at various initial speeds. With what minimum initial speed vesc will the rocks need to be thrown in order for them never to "fall" back to the asteroid? Assume that the asteroid is approximately spherical, with an average density p 3.06 x 106 g/m³ and volume V = 3.32 x 1012 m³. Recall that the universal gravitational constant is G : 6.67 x 10-11 N-m²/kg².An object is projected from the surface of the earth with a speed of 2.72×104 m/s. What is its speed when it is very far from the earth? (Neglect air resistance.)
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- A bowling ball of mass m = 1.6 kg is resting on a spring compressed by a distance d = 0.36 m when the spring is released. At the moment the spring reaches its equilibrium point, the ball is launched from the spring into the air in projectile motion at an angle of θ = 38° measured from the horizontal. It is observed that the ball reaches a maximum height of h = 3.5 m, measured from the initial position of the ball. Let the gravitational potential energy be zero at the initial height of the bowling ball. a. What is the spring constant k, in newtons per meter? b. Calculate the speed of the ball, vo in m/s, just after the launch.Jupiter's moon Io has active volcanoes (in fact, it is the most volcanically active body in the solar system) that eject material as high as 500 km (or even higher) above the surface. Io has a mass of 8.93×1022kg and a radius of 1821 km. For this calculation, ignore any variation in gravity over the 500 km range of the debris. How high would this material go on earth if it were ejected with the same speed as on Io?You are designing a single-stage rocket to launch a 300-kg satellite. Assume the rocket engine's I, as 460 sec. Use g=9.8 m/sec² for the gravity acceleration constant. sp (a) Assume that you are launching the satellite in free space with no gravity and no aerodynamic drag, and your rocket has zero mass except the pronellants and the satellite. Calculate the mass of the propellants to give AV = 7.784 km/sec. (b) Assume the same in (a) except that the rocket's mass is proportional to the propellants: 15% of the propellants. Calculate the mass of the propellants for AV=7.784 km/sec. (Of course, the rocket's mass remains the same after the burn)
