A 2160-kg test rocket is launched vertically from the launch pad. Its fuel (of n

Question

A 2160-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 1.00 m/s2 and 2.00 s later an upward velocity of 2.50 m/s . 1) Determine A? 2) Determine B 3) At 3.70s after fuel ignition, what is the acceleration of the rocketket? 4) What thrust force does the burning fuel exert on it, assume no air resistance. Express the thrust as a multiple of the rockets weight. 5) What was the initial thrust due to the fuel.

Explanation / Answer

Given V=At+Bt2

acceleration

a=dV/dt =A+2Bt

at t=0=>a=1 m/s2

1=A+0

A=1

b)

at t=2 s=>V=2.5 m/s

2.5=1*2+B*22

B=0.125

c)

at t=3.7s

a=1+2*0.125*3.7

a=1.925 m/s2

d)

T=m(a-g)=2160(1.925-(-9.81))

T=25347.6 N

in terms of rocket weight

T=(25347.6/2160*9.81)*W=1.2W

e)

T=2160(1+9.81)=23349.6 N

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