A 2.44×104-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 18.9-N instrument hangs from a wire that can support a maximum tension of 44.1 N .7

How far is the rocket above the earth's surface when it breaks the sound barrier? Find the minimum time for this rocket to reach the sound barrier (330 m/s) without breaking the inside wire. Find the maximum vertical thrust of the rocket engines under these conditions.

 x = 2381.2 m ,    t = 14.43 s ,  I = 8.05 10⁶ N s

Explanation:

a) to find the distance to break the sound barrier (v = 330 m / s) we use the kinematic relationship

           v² = v₀² + 2 a x

To find the acceleration suppose the rocket does not break the wire that holds the load, so we can use the second Newton law to find the maximum acceleration

            T = m a

            a = T / m

Body mass and weight is related

           W = mg

           m = W / g

           a = T g / W

           a = 44.1   9.8 / 18.9

           a = 22,867 m / s²

Let's look for the distance if part of the rest

          x = v² / 2 a

          x = 330² /(2  22,867)

          x = 2381.2 m

.b) the time to break this barrier

          v = v₀ + a t

          t = v / a

          t = 330 / 22,867

          t = 14.43 s

c) the thrust is

          I = Δp

          I = m –m v₀

          I = 2.44 10⁴ 330 -0

          I = 8.05 10⁶ N s