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,

$\begin{gathered} 144.4=182.8\times a \\ a=\frac{144.4}{182.8} \\ a=0.7899ms^{-2} \end{gathered}$

By the kinematic equations,

$v-u=at$

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

Substituting the known values,

$\begin{gathered} v-0=0.7899\times1.19 \\ v=0.94ms^{-1} \end{gathered}$

The average speed of the astronaut is,

$\begin{gathered} s_{average}=\frac{v+u}{2} \\ =\frac{0.94+0}{2} \\ =0.47ms^{-1} \end{gathered}$

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

$\begin{gathered} s_{average}=0.47\times\frac{10^{-3}^{}^{}}{\frac{1}{60\times60}} \\ s_{average}=0.47\times60\times60\times10^{-3} \\ s_{average}=1.692kmh^{-1} \end{gathered}$

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