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PROBLEM 14.89
A toy car is propelled by water that squirts from an internal
tank at a constant 6 ft/s relative to the car. The weight of the
empty car is 0.4 lb and it holds 2 lb of water. Neglecting other
tangential forces, determine the top speed of the car.
PROBLEM 14.90
A toy car is propelled by water that squirts from an internal
tank. The weight of the empty car is 0.4 lb and it holds 2 lb of
water. Knowing the top speed of the car is 8 ft/s, determine the
relative velocity of the water that is being ejected.
PROBLEM 14.91
The main propulsion system of a space shuttle consists of three identical
rocket engines which provide a total thrust of 6 MN. Determine the rate at
that the hydrogen-oxygen propellant is burned by each of the three
engines, knowing that it is ejected with a relative velocity of 3750 m/s.
PROBLEM 14.92
The main propulsion system of a space shuttle consists of three identical
rocket engines, each of which burns the hydrogen-oxygen propellant at
the rate of 750 lb/s and ejects it with a relative velocity of 12000 ft/s.
Determine the total thrust provided by the three engines.
PROBLEM 14.93
A rocket sled burns fuel at the constant rate of 120
lb/s. The initial weight of the sled is 1800 lb,
including 360 lb of fuel. Assume that the track is
lubricated and the sled is aerodynamically designed
so that air resistance and friction are negligible. (a)
Derive a formula for the acceleration a of the sled as
a function of time t and the exhaust velocity vex of the
burned fuel relative to the sled. Plot the ratio a/vex
versus time t for the range 0 < t < 4 s, and check the
slope of the graph at t = 0 and t = 4 s using the
formula for a. (b) Determine the ratio of the velocity
vb of the sled at burnout to the exhaust velocity vex.
PROBLEM 14.93 (Continued
PROBLEM 14.94
A space vehicle describing a circular orbit at a speed of 3
24 10 km/h
releases its front end, a capsule that has a gross mass of 600 kg,
including 400 kg of fuel. If the fuel is consumed at the rate of 18 kg/s
and ejected with a relative velocity of 3000 m/s, determine (a) the
tangential acceleration of the capsule as the engine is fired, (b) the
maximum speed attained by the capsule.
PROBLEM 14.95
A 540-kg spacecraft is mounted on top of a rocket with a mass of 19 Mg, including 17.8 Mg of fuel.
Knowing that the fuel is consumed at a rate of 225 kg/s and ejected with a relative velocity of 3600
m/s, determine the maximum speed imparted to the spacecraft if the rocket is fired vertically from the
ground.
PROBLEM 14.96
The rocket used to launch the 540-kg spacecraft of Problem 14.95 is redesigned to include two
stages A and B, each of mass 9.5 Mg, including 8.9 Mg of fuel. The fuel is again consumed at a rate
of 225 kg/s and ejected with a relative velocity of 3600 m/s. Knowing that when stage A expels its
last particle of fuel its casing is released and jettisoned, determine (a) the speed of the rocket at that
instant, (b) the maximum speed imparted to the spacecraft.
PROBLEM 14.97
The weight of a spacecraft, including fuel, is 11,600 lb when the rocket engines are
fired to increase its velocity by 360 ft/s. Knowing that 1000 lb of fuel is consumed,
determine the relative velocity of the fuel ejected.
