A 2590-kg test rocket is launched vertically from the launch pad. Its fuel (of n

Question

A 2590-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 1.25 m/s2 and 1.00 s later an upward velocity of 2.05 m/s.

(a) Determine A and B, including their SI units.

(b) At 4.00 s after fuel ignition, what is the acceleration of the rocket?
m/s2 ?

(c) What thrust force does the burning fuel exert on it, assume no air resistance? Express the thrust in newtons and as a multiple of the rocket's weight.
T =  N ?
T =  *w ?

(d) What was the initial thrust due to the fuel?
N ?

Explanation / Answer

v(t) = At + Bt^2

a(t) = dv/dt = A+2Bt

at t=0 , a(0) = 1.25

1.25 = A + 0

A = 1.25

v(1) = 2.05 = 1.25 + B*1

B = 2.05-1.25 = 0.8

A = 1.25 , B = 0.8

b)a(t) = A + 2Bt

a(4) = 1.25 + 2*0.8*4

a(4) = 7.65 m/s2

c) thrust force = mg+ma = 2590*(9.8+7.65) = 45195.5 N

weight of the rocket = 2590*9.8 = 25382 N

T/W = 45195.5/25382

T = 1.78 W

d) initial thrust = mg + ma

initial thrust = 2590 * (9.8+1.25) = 28619.5 N

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.