Question

An 80 kg spacewalking astronaut pushes off a 640 kg satellite,exerting a 100 N force for the 0.50 s it takes him to straighten hisarms. How far apart are the astronaut and the satellite after 1.0 min?

Answer 1

Step-by-step explanation

Step 1

Let

`\begin{gathered} mass\text{ of astronaut=80 Kg} \\ mass\text{ of satellite=640 Kg} \\ \text{force exerted by the satellite=}100\text{ N} \\ time=0.5\text{ s} \end{gathered}`

so

a)Determine the acceleration of the satellite after the push

`\begin{gathered} F=ma \\ a=(F)/(m) \\ \text{replace} \\ a=\frac{100\text{ N}}{640\text{ Kg}}=0.15625\text{ }(m)/(s^2) \\ a_(satellite)=0.15625\text{ }(m)/(s^2) \end{gathered}`

b) get the final velocity of the satellite

`\begin{gathered} v=u+at \\ so \\ v=0+0.15625(m)/(s^2)\cdot0.5 \\ v=0.078125\text{ }(m)/(s) \\ u=o,\text{because the initial sp}eed\text{ is zero} \end{gathered}`

Step 2

finally,find the displacement of the satellite after 1 m

1minute = 60 s

`\begin{gathered} d_1=v\cdot t \\ d_1=0.078125(m)/(s^2)\cdot60s \\ d_1=4.6875\text{ m} \end{gathered}`

so,the answer is

4.6875