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Help with mastering physics problem 5.138: vertical rocket launch with instrument hanging inside at constant acceleration.?

A 2.60×104-kg rocket blasts off vertically from the earth's surface with a constant acceleration. During the motion considered in the problem, assume that g remains constant. Inside the rocket, a 17.3-N instrument hangs from a wire that can support a maximum tension of 27.7 N

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

Part B
Find the maximum vertical thrust of the rocket engines under these conditions.

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

Below is the recommendation and reference answer for question "Help with mastering physics problem 5.138: vertical rocket launch with instrument hanging inside at constant acceleration.?" It was collected and sorted by the editor of this site but not sure the answer is entirely accurate.

A) find the kinematic acceleration:
27.7 N = 17.3N * (9.8m/s² + a) / 9.8m/s²
a = 5.89 m/s²

and now use v = a*t
t = v / a = 330m/s / 5.89m/s² = 56.0 s ◄

B) The thrust must not only provide the kinematic acceleration but must also support the weight as well:
F = m(g + a) = 2.60e4kg * (9.8 + 5.89)m/s² = 4.08e5 N ◄

C) h = ½at² = ♂ * 5.89m/s² * (56.0s)² = 9240 m ◄
OR
h = v² / 2a = (330m/s)² / 2*5.89m/s² = 9240 m

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