Chapter 11: Q. 73 (page 291)

A rocket in deep space has an empty mass of 150 kg and exhausts the hot gases of burned fuel at 2500 m/s. It is loaded with 600 kg of fuel, which it burns in 30 s. What is the rocket’s speed 10 s, 20 s, and 30 s after launch?

Short Answer

Expert verified

At t = 10s, speed is equal to 775.5 m/s

At t = 20s, speed is equal to 1905.3 m/s

At t = 30s, speed = v_max = 4023.5 m/s

Step by step solution

Step 1. Given information is Empty mass of Rocket mR = 150 kgMass of fuel mFO = 600 kgTime taken to burn the fuel∆t=30 sExhaust speed vex = 2500 m/s

We need to calculate the rocket’s speed 10 s, 20 s, and 30 s after launch.

Step 2. Using the rate of burning fuel to find out the rocket's speed after launch.

Rate of burning fuel :

$R = \frac{d m}{d t} = \frac{600}{30} = 20 k g / s M a s s o f f u e l b u r n e d i n g i v e n t i m e i n t e r v a l : m' = \int_{0}^{t} R . d t = R t M a s s o f f u e l r e m a i n i n g a f t e r t h a t t i m e : m'' = m_{F O} - R T H e n c e, t h e t o t a l w e i g h t o f t h e r o c k e t i s, m = m'' + m_{R} m_{0} = m_{R} + m_{F O} = (150 + 600) k g = 750 k g W e k n o w t h a t, v = v_{e x} \ln \frac{m_{0}}{m} F o r t = 10 s m'' = m_{F O} - R t = 600 - (20 \times 10) = 400 k g m = m'' + m_{R} = (400 + 150) k g = 550 k g v = 2500 \ln \frac{750}{550} v = 775.5 m / s F o r t = 20 s m'' = m_{F O} - R t = 600 - 20 \times 20 = 200 k g m = m'' + m_{R} = (200 + 150) k g = 350 k g v = 2500 \ln \frac{750}{350} v = 1905.3 m / s F o r t = 30 s m'' = m_{F O} - R t = 600 - 20 \times 30 = 0 I t m e a n s t h e r o c k e t w i l l a c h i e v e m a x i m u m v e l o c i t y U \sin g f o r m u l a, v_{m a x} = v_{e x} \ln \frac{m_{F O} + m_{R}}{m_{R}} v_{m a x} = 2500 \ln \frac{750}{150} = 4023.5 m / s$

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A rocket in deep space has an empty mass of 150 kg and exhausts the hot gases of burned fuel at 2500 m/s. It is loaded with 600 kg of fuel, which it burns in 30 s. What is the rocket’s speed 10 s, 20 s, and 30 s after launch?

Short Answer

Step by step solution

Step 1. Given information is Empty mass of Rocket mR = 150 kgMass of fuel mFO = 600 kgTime taken to burn the fuel∆t=30 sExhaust speed vex = 2500 m/s

Step 2. Using the rate of burning fuel to find out the rocket's speed after launch.

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