Consider a rocket that is in deep space and at rest relative to an inertial reference frame. The rocket's engine is to be fired for a certain interval. What must be the rocket's *mass ratio* (ratio of initial to final mass) over that interval if the rocket's final speed relative to the inertial frame is to be equal to (a) the exhaust speed (speed of the exhaust products relative to the rocket) and (b) 3.00 times the exhaust speed? (The exhaust products from the rocket escape at a constant velocity relative to the rocket)(a) - Number [Input box]- Units [Dropdown menu](b) - Number [Input box]- Units [Dropdown menu]

From differential equation of rocket motion we have,v2-v1=u lnm∘mfwhere,u is the speed of the…

Answered: Consider a rocket that is in deep space…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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A firework with mass M is launched from the origin with initial speed v0 and angle θ0 and travels along the usual parabolic path above flat ground. At the peak of its path, it explodes into two pieces. Piece one has mass .5M and speed v1 in an angle of 30◦ below the horizontal direction and the other piece has mass .5M and speed v2 in an unknown direction. (a) Do the two pieces land at the same time? (Justify your answer) (b) Sketch the motion of the COM and of both pieces. Note any external forces, and describe if p is conserved in x, y or both for the duration of the flight. Also note if the two pieces land at the same distance from the target or describe which one lands closer/further.
Problem 3: A particle with mass ma = 3.00 kg is located at ra = (2.50 i + 3.50 j) m, and a second particle of mass m2B = 5.00 kg is located at rB = (1.50 i - 3.00 j) m. Find the location of the center of mass of the system relative to the point (1,1).
A rocket, which is in deep space and initially at rest relative to an inertial reference frame, has a mass of 72.9 x 105 kg, of which 14.7 x 10° kg is fuel. The rocket engine is then fired for 300 s, during which fuel is consumed at the rate of 360 kg/s. The speed of the exhaust products relative to the rocket is 3.82 km/s. (a) What is the rocket's thrust? After the 300 s firing, what are (b) the mass and (c) the speed of the rocket? (a) Number i Units (b) Number Units (c) Number i Units
The Merlin rocket engines developed by SpaceX can produce 7.12 ✕ 105 N of instantaneous thrust with an exhaust speed of 3.05 ✕ 103 m/s in vacuum. What mass of fuel does the engine burn each second to produce this thrust? (Enter your answer in kg/s.)
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A rocket, which is in deep space and initially at rest relative to an inertial reference frame, has a mass of 78.4 × 105 kg, of which 8.68 × 105 kg is fuel. The rocket engine is then fired for 340 s, during which fuel is consumed at the rate of 340 kg/s. The speed of the exhaust products relative to the rocket is 3.78 km/s. (a) What is the rocket's thrust? After the 340 s firing, what are (b) the mass and (c) the speed of the rocket? (a) Number 1290000 Units N (b) Number 7720000 Units kg (c) Number 3830 Units m/s
A space vehicle is traveling at 4450 km/h relative to the Earth when the exhausted rocket motor is disengaged and sent backward with a speed of 64 km/h relative to the command module. The mass of the motor is four times the mass of the module. What is the speed (km/h) of the command module relative to Earth after the separation?
Ion-propulsion rockets have been proposed for use in space. They employ atomic ionization techniques and nuclear energy sources to produce extremely high exhaust velocities, perhaps as great as 8.00 ✕ 106 m/s. These techniques allows a much more favorable payload-to-fuel ratio. To illustrate this fact: (a) Calculate the increase in velocity in m/s of a 23,000-kg space probe that expels only 40.0-kg of its mass at the given exhaust velocity. m/s (b) These engines are usually designed to produce a very small thrust for a very long time—the type of engine that might be useful on a trip to the outer planets, for example. Calculate the acceleration in m/s2 of such an engine if it expels 4.50 ✕ 10−6 kg/s at the given velocity, assuming the acceleration due to gravity is negligible. m/s2
Pluto and its satellite Charon have masses which are more similar to each other than any other knonw pair of orbiting bodies in the Solar system. How far from the center of pluto is the barycenter or center of mass of the Pluto-Charon system? Take the mass of Pluto to be 1.31 × 10^22 kg, and 1.59 × 10^21 kg for Charon (about one eighth that of Pluto). Assume Pluto and its moon Charon are separated by 19,640 km while the radius of Pluto and Charon are 1190 km and that of Charon are 606 km respectively. Treating Pluto and Charon as spherically symmetric objects, how far from Pluto is the barycenter of the Pluto - Charon pair, and is this point inside are outside of Pluto? Hint: Place Pluto at the origin and Charon on the x axis. A. 289 km; inside B. 781 km; inside C. 2130 km; outside D. 5910 km; outside
If a rocket engine ejects gases at a rate of 29 kg/s, how fast must the gaseous exhaust be moving if the thrust produced is sufficient to allow a 2.7 x 105 kg rocket to rise slowly from the earth when aimed straight up? Express your answer in km/s.
A space is traveling at 4300 km/hr relative to Earth. When the exhausted rocket motor is. disengaged. and sent backward with a speed of 82 km/hr relative to the command module. The mass of the rocket motor is 4 time the mass of the module. What is the speed of the command module relative to the earth just after the separation. Answer in km/hr.

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