contestada

A 95-kg astronaut and a 1300-kg satellite are at rest relative to the space shuttle. The astronaut pushes on the satellite, giving it a speed of 0.17 m/s directly away from the shuttle. Seven-and-a-half seconds later the astronaut comes into contact with the shuttle.
What was the initial distance from the shuttle to theastronaut?

Respuesta :

davidlcastiblanco

Answer:

[tex]d=17.44 m[/tex]

Explanation:

Conservation of Momentum. Momentum is said to be conserved when there is zero net external force acting on the object.

So mathematically:  

Definition of momentum: [tex]p = m*v[/tex]

Newton's 1st law: [tex]F = m*a[/tex] ⇒[tex]m*\frac{dv}{dt}=\frac{dp}{dt}[/tex]

Net external force is zero: [tex]F = 0[/tex]⇒ [tex]\frac{dv}{dt}=0[/tex]=Dp=0

Conservation of Momentum is mathematically expressed as:

mv(initial)  = mv(final)

Hence in this case:

[tex]v=0.17 \frac{m}{s}[/tex]

by conservation of energy:

[tex]m_{s}*v_{s}=m_{a}*v_{a}[/tex]

[tex]1300kg*0.17 \frac{m}{s}=95kg*m_{a}[/tex]

[tex]m_{a}=2.326\frac{m}{s}[/tex]

[tex]m_{a}=\frac{d}{t}[/tex]

[tex]d=m_{a}*t[/tex]

[tex]d=2.32\frac{m}{s}*7.5s[/tex]

[tex]d=17.44 m[/tex]

Otras preguntas