Question

A 4.75 • 105-kg rocket is accelerating straight up. Its engines produce 1.5 • 107 N of thrust, and air resistance is 4.7 • 106 N . find acceleration using coordinate system where up is positive.

Answer 1

The free body diagram of the rocket can be shown as,

According to free body diagram, the net force acting on the rocket is given as,

`F=T-f-mg`

According to Newton's law,

`F=ma`

Plug in the known value,

`\begin{gathered} ma=T-f-mg \\ a=(T-f-mg)/(m) \end{gathered}`

Substitute the known values,

`\begin{gathered} a=\frac{1.5*10^7\text{ N-}4.7*10^6\text{ N-(4.75}*10^5kg)(9.8m/s^2)(\frac{1\text{ N}}{1kgm/s^2})}{4.75*10^5\text{ kg}} \\ =\frac{1.5*10^7\text{ N-}0.47*10^7\text{ N-}0.47*10^7\text{ N}}{4.75*10^5\text{ kg}} \\ =\frac{0.56*10^7\text{ N}}{4.75*10^5\text{ kg}}(\frac{1kgm/s^2}{1\text{ N}}) \\ \approx11.8m/s^2 \end{gathered}`

Thus, the acceleration of the rocket is 11.8 m/s2.