Question

An astronaut and equipment has a total mass of 182.8 kg. While initially at rest inspace, the astronaut fires a 144.4 newton rocket for 1.190 seconds. What is theaverage speed of the astronaut (in km/h)?

Answer 1

Given data:

* The total mass of an astronaut and equipment is,

`m=182.8\text{ kg}`

* The force is given as,

`F=144.4\text{ N}`

* The time taken is,

`t=1.19\text{ s}`

Solution:

According to the Newton's second law,

`F=ma`

where a is the acceleration of the body,

Substituting the known values,

`\begin{gathered} 144.4=182.8* a \\ a=(144.4)/(182.8) \\ a=0.7899ms^(-2) \end{gathered}`

By the kinematic equations,

`v-u=at`

where u is the initial velocity and v is the final velocity,

Substituting the known values,

`\begin{gathered} v-0=0.7899*1.19 \\ v=0.94ms^(-1) \end{gathered}`

The average speed of the astronaut is,

`\begin{gathered} s_(average)=(v+u)/(2) \\ =(0.94+0)/(2) \\ =0.47ms^(-1) \end{gathered}`

The average speed of the astronaut in Km/h is,

`\begin{gathered} s_(average)=0.47*\frac{10^(-3)^{}^{}}{(1)/(60*60)} \\ s_(average)=0.47*60*60*10^(-3) \\ s_(average)=1.692kmh^(-1) \end{gathered}`

Thus, the average speed of the astronaut is 1.692 km/h.