A 2320-kg test rocket is launched vertically from the launch pad. Its fuel (of n

Question

A 2320-kg test rocket is launched vertically from the launch pad. Its fuel (of negligible mass) provides a thrust force so that its vertical velocity as a function of time is given by v(t) = At + Bt2 where A and B are constants and time is measured from the instant the fuel is ignited. At the instant of ignition, the rocket has an upward acceleration of 2.00 m/s2 and 2.00 s later an upward velocity of 2 07 m/s. At 3.70 s after fuel ignition, what is the acceleration of the rocket? At 3.70 s after fuel ignition what thrust force does the burning fuel exert on it assume on it assume no air resistance?

Explanation / Answer

dV/dt = A + 2Bt

at t=0 acc= 2 => A= 2

at t=2 veleocity= 2.07 => A*2+B*4 = 2.07

=> B*4 = 2.07 - 4

=> B = (2.07 - 4)/4 = -0.482

at 3.70 sec

acc = 2*2 - -0.482*4 = 2.072m/s^2

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