A 2500-kg test rocket is launchedvertically from the launch pad. Its fuel (of ne

Question

A 2500-kg test rocket is launchedvertically from the launch pad. Its fuel (of negligible mass)provides a thrust force so that its vertical velocity as a functionof time is given by v(t) = At +Bt2, where A and B areconstants and time is measured from the instant the fuel isignited. At the instant of ignition, the rocket has an upwardacceleration of 1.60 m/s2and 1.00 s later an upward velocity of 2.05 m/s.
(a) Determine A and B,including their SI units.
A = B =
(b) At 4.00 s after fuel ignition, what is the acceleration of therocket?


(c) What thrust force does the burning fuel exert on it, assume noair resistance? Express the thrust in newtons and as a multiple ofthe rocket's weight.
T =
T =

(d) What was the initial thrust due to the fuel?
(a) Determine A and B,including their SI units.
A = B =
(b) At 4.00 s after fuel ignition, what is the acceleration of therocket?


(c) What thrust force does the burning fuel exert on it, assume noair resistance? Express the thrust in newtons and as a multiple ofthe rocket's weight.
T =
T =

(d) What was the initial thrust due to the fuel?
A = B =

Explanation / Answer

(a) Determine A and B,including their SI units.
looking at the equation for velocity v, A is in m/s^2 and B is inm/s^3.
a(t) = dv/dt = A + 2Bt
a(0) = A = 1.6 m/s^2
v(1) = A + B = 2.05
B = 0.45 m/s^3
(b) At 4.00 s after fuel ignition, what is the acceleration of therocket?
a(4) = 1.6 + 2*0.45*4 = 5.2 m/s^2
(c) What thrust force does the burning fuel exert on it, assume noair resistance? Express the thrust in newtons and as a multiple ofthe rocket's weight.
T = ma = 2500*5.2 = 13000 N
since rocket weight is 2500*9.8 = 24500 N,
T = (13000/24500) times rocket weight or .53 times rocketweight.
(d) What was the initial thrust due to the fuel?
initial thrust = 2500*1.6 = 4000 N.

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