The first stage of a space vehicle consumed fuel and oxidizer atthe rate of 2.20

Question

The first stage of a space vehicle consumed fuel and oxidizer atthe rate of 2.20 x 104kg/s, with an exhaust speed of 3.25 x103 m/s. (a) Calculate the thrust produced by theseengines.
1 N
(b) Find the acceleration of the vehicle just as it lifted off thelaunch pad on the Earth if the vehicle's initial mass was3.00 x 106 kg. [Note: You must include the force ofgravity to solve part (b).]
2 m/s2 upward (a) Calculate the thrust produced by theseengines.
1 N
(b) Find the acceleration of the vehicle just as it lifted off thelaunch pad on the Earth if the vehicle's initial mass was3.00 x 106 kg. [Note: You must include the force ofgravity to solve part (b).]
2 m/s2 upward

Explanation / Answer

(a). Thrust produced by these engines F = Rate of fuelconsumed * exhaust speed                                                              = 2.2* 10 ^ 4 kg / s * 3.25 * 10 ^ 3 m / s                                                              = 7.15 * 10 ^ 7 N (b). Initial mass m = 3 * 10 ^ 6 kg Accleration a = ( F -mg ) / m                     = [ 7.15 * 10 ^ 7 - ( 3 * 10 ^ 6 * 9.8 ) ] / ( 3 * 10 ^ 6 )                     = [ 7.15 * 10 ^ 7 - 2.94 * 10 ^ 7 ] /3* 10 ^ 6                     = 14.033 m / s ^ 2

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