A rocket, initially at rest on the ground, accelerates straight upward from rest with constant (net) acceleration 29.4 m/s2 m / s 2 . The acceleration period lasts for time 7.00 s s until the fuel is exhausted. After that, the rocket is in free fall.

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CarliReifsteck CarliReifsteck · Answer 1 · 2020-10-08T00:05:08+02:00

Answer:

The maximum height is 2881.2 m.

Explanation:

Given that,

Acceleration = 29.4 m/s²

Time = 7.00 s

We need to calculate the distance

Using equation of motion

[tex]s=ut+\dfrac{1}{2}at^2[/tex]

Put the value into the formula

[tex]s=0+\dfrac{1}{2}\times29.4\times7^2[/tex]

[tex]s=720.3\ m[/tex]

We need to calculate the velocity

Using formula of velocity

[tex]v=a\times t[/tex]

Put the value into the formula

[tex]v=29.4\times7[/tex]

[tex]v=205.8\ m/s[/tex]

We need to calculate the height

Using formula of height

[tex]H=\dfrac{v^2}{2g}[/tex]

Put the value into the formula

[tex]H=\dfrac{(205.8)^2}{2\times9.8}[/tex]

[tex]H=2160.9\ m[/tex]

We need to calculate the maximum height

Using formula for maximum height

[tex]H'=H+s[/tex]

Put the value into the formula

[tex]H'=2160.9+720.3[/tex]

[tex]H'=2881.2\ m[/tex]

Hence, The maximum height is 2881.2 m.