(a)
Find the altitude at which stage A of the rocket is released.
(a)
Answer to Problem 14.102P
The altitude at which stage A of the rocket is released is
Explanation of Solution
Given information:
Consider the initial mass of the rocket is denoted by
The rate of consumption of the fuel is denoted by q.
The velocity of the rocket after time t is denoted by v.
The acceleration due to gravity is denoted by g.
Refer Problem 14.96.
The mass of the rocket is
The mass of the stage A and B is
Show the unit conversion of the mass as follows:
The rate of fuel consumption is
The relative velocity of the rocket is
Calculation:
Show the thrust force (P) of the rocket as follows:
Show the combined mass (m) of the rocket and the unspent fuel as follows:
Show the weight force (W) as follows:
Show the acceleration (a) of the rocket as follows:
Modify Equation (3) using (2) and (1).
Show the velocity of the rocket as follows:
Integrate above Equation with respect to time.
Show the displacement of the rocket as follows:
Integrate above Equation with respect to time.
Consider the value of z as follows:
Differentiate the above Equation with respect to time t.
Consider the value of the
Substitute
Modify Equation (4) using Equation (5) and (6).
Take the lower and upper limit of the integral as
Substitute 1 for
The mass of the fuel is
The velocity of the rocket is
The rate of the fuel consumption is
Calculate the time taken (t) as follows:
Consider the first stage:
The initial velocity and initial distance covered are
Calculate the initial mass of the rocket
Calculate the final velocity of the rocket using the relation:
Substitute 0 for
Calculate the altitude
Substitute 0 for
Thus, the altitude
(b)
Find the altitude at which the fuel of both stages are consumed.
(b)
Answer to Problem 14.102P
The altitude at which the fuel of both stages are consumed is
Explanation of Solution
Given information:
Calculation:
Consider the fuel of both the stages are consumed.
Calculate the final mass
Calculate the altitude
Substitute
Thus, the altitude
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Chapter 14 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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