A 2.52×10 4 -kg rocket blasts off vertically from the earth\'s surface with a co

Question

A 2.52×104-kg rocket blasts off vertically from the earth's surface with a constant acceleration. During the motion considered in the problem, assume thatg remains constant. Inside the rocket, a 15.8-Ninstrument hangs from a wire that can support a maximum tension of 29.0 N .

a). Find the minimum time for this rocket to reach the sound barrier (330m/s) without breaking the inside wire.

b). Find the maximum vertical thrust of the rocket engines under these conditions.

c). How far is the rocket above the earth's surface when it breaks the sound barrier?

Explanation / Answer

m = 25200 kg

weight of instrument = 15.8 N

mass of instrument = 15.8/9.8 = 1.61 kg

maximum tension that the wire can support = 29 N

Let the maximum acceleration for which wire will not break = a

Then 29 >= 1.61*(g+a)

=> amax = 6 m/s2

So time to reach speed of 330 m/s will be given by

v = u + at

=> 330 = 0 + 6t

=> t = 55 s

a) minimum time for this rocket to reach the sound barrier (330m/s) without breaking the inside wire = 55 s

b) maximum vertical thrust of the rocket engines under these conditions = m * (g+a) = 25200*(9.8+6) = 398160 N

c) Rocket's height when it breaks the sound barrier = ut + 0.5at2 = 0 + 0.5*6*552 = 9075 m

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