The first state of amultistage rocket boosts the rocket to a speed of 0.1 relative to the ground before being jettisoned. The next stage boosts the rocket to a speed of 0.1 relative to the final speed of the first stage, and so on. How many stages does it take to boost the payload to a speed in excess of 0.95 relative to the ground?
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- 1. Consider a mass m initially at rest at a large distance I from center of the earth (l>R the earth's radius). The mass m is released and falls toward the earth. (a) Calculate the speed of the mass as a function of its distance x from the center of the earth. (b) In the approximation that l>>R, how much time does it take for the mass m to reach the earth? Express your answers in terms of R, 1, g (acceleration at the earth's surface) and (for part a) x.I. With external gravitational field In this second part you are asked to analyze rocket propulsion with the present of gravitational field g. This appears for instance when the rocket is launching from the surface of a planet. (1) Describes why you are not allowed to use the momentum conservation here. (2) Evaluate the speed of the rocket measure by inertial observer on the ground as a function of time v(t) if the speed of the gas propulsion with respect to the rocket is vret and the burning rate is constant constant! dm dt (3) Plot v(t) that you obtained from point (2) above, for three different values of gravitational field (assuming similar initial mass), which is: Imoon = 1.62 m/s? • Gearth = 9.81 m/s? Ijupiter = 24.79 m/s? in a single plot, if the burn dm ate is constant = 1500 kg/s. Analyze your result and dt describes how the speed increases for each situation! 20:18 Ai 11/03/2022Suppose we are given the values for the two masses and their initial velocities along with the final velocity of B as follows: ??=1.2;??,??=5.7???=2.7; ??,??=2.3??????,??=4.1? What is the final velocity (speed and direction) of mass A?
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