Concept explainers
Determine the distance traveled by the spacecraft of Prob. 14.97 during the rocket engine firing, knowing that its initial speed was 7500 ft/s and the duration of the firing was 60 s.
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.
Fig. P14.97 and P14.98
Find the distance travelled by the spacecraft.
Answer to Problem 14.99P
The distance travelled by the spacecraft is
Explanation of Solution
Given information:
The initial speed of the spacecraft is
The duration of firing is
The change in velocity is
The gross weight of the spacecraft is
The fuel consumed rate is
Calculation:
Calculate the thrust force
Calculate the mass
Calculate the acceleration
Substitute
Substitute
Calculate the velocity
Substitute
Calculate the displacement
Integrate both sides of the Equation (2) as shown below.
Consider
Differentiate both sides of the Equation (4) as shown below.
Substitute z for
Substitute
Calculate the velocity
Substitute
Consider the acceleration due to gravity
Calculate the gross mass of the spacecraft
Substitute
Consider that the mass of the fuel
Substitute
Calculate the mass
Substitute
Consider the initial displacement
Calculate the relative velocity
Substitute
Calculate distance travelled by the spacecraft
Substitute
Therefore, the distance travelled by the spacecraft is
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