A rocket moving in outer space maintains a constant acceleration (magnitude = 20 m/s2) while ejecting fuel at a speed of 15 km/s relative to the rocket. If the initial mass of the rocket is 3 000 kg, what is the magnitude of the thrust after 800 kg of fuel have been consumed?
a. 56 kN
b. 48 kN
c. 52 kN
d. 44 kN
e. 36 kN
[Ques. 2] A rocket with an initial mass of 1000 kg adjusts its thrust by varying the rate at which mass is ejected. The ejection speed relative to the rocket is 40 km/s. If the acceleration of the rocket is to have a magnitude of 20 m/s2 at an instant when its mass is 80 of the original mass, at what rate is mass being ejected at that instant? Ignore any external forces on the rocket.
a. 0.40 kg/s
b. 0.50 kg/s
c. 0.60 kg/s
d. 0.70 kg/s
e. 0.80 kg/s
[Ques. 3] A rocket engine consumes 450 kg of fuel per minute. If the exhaust speed of the ejected fuel is 5.2 km/s, what is the thrust of the rocket?
a. 42 kN
b. 39 kN
c. 45 kN
d. 48 kN
e. 35 kN
[Ques. 4] Three particles are placed in the xy plane. A 40-g particle is located at (3, 4) m, and a 50-g particle is positioned at (2, 6) m. Where must a 20-g particle be placed so that the center of mass of this three-particle system is located at the origin?
a. (1, 3) m
b. (1, 2) m
c. (1, 12) m
d. (1, 7) m
e. (1, 3) m
[Ques. 5] At an instant when a particle of mass 80 g has a velocity of 25 m/s in the positive y direction, a 75-g particle has a velocity of 20 m/s in the positive x direction. What is the speed of the center of mass of this two-particle system at this instant?
a. 16 m/s
b. 45 m/s
c. 23 m/s
d. 20 m/s
e. 36 m/s
[Ques. 6] At an instant when a particle of mass 50 g has an acceleration of 80 m/s2 in the positive x direction, a 75-g particle has an acceleration of 40 m/s2 in the positive y direction. What is the magnitude of the acceleration of the center of mass of this two-particle system at this instant?
a. 60 m/s2
b. 56 m/s2
c. 40 m/s2
d. 50 m/s2
e. 46 m/s2
[Ques. 7] A pitcher claims he can throw a baseball with as much momentum as a 3.00-g bullet moving with a speed of 1500 m/s. A baseball has a mass of 0.145 kg. What must be its speed if the pitcher's claim is valid?
[Ques. 8] The value of the momentum of a system is the same at a later time as at an earlier time if there are no
a. collisions between particles within the system.
b. inelastic collisions between particles within the system.
c. changes of momentum of individual particles within the system.
d. internal forces acting between particles within the system.
e. external forces acting on particles of the system.
[Ques. 9] The law of conservation of momentum applies to a collision between two bodies since
a. they exert equal and opposite forces on each other.
b. they exert forces on each other respectively proportional to their masses.
c. they exert forces on each other respectively proportional to their velocities.
d. they exert forces on each other respectively inversely proportional to their masses.
e. their accelerations are proportional to their masses.
[Ques. 10] A ball falls to the ground from height h and bounces to height h'. Momentum is conserved in the ball-earth system
a. no matter what height h' it reaches.
b. only if h' < h.
c. only if h' = h.
d. only if h' > h.
e. only if h' h.
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