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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? .

## 1 Answers

• 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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