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An astronaut floating at rest in space has run out of fuel in her jetpack. Sherealizes that throwing tools from her toolkit in the opposite direction will helppropel her back toward the space station. If the astronaut has a mass of 91kg and she throws a hammer of mass 4 kg at a speed of 3.5 m/s, what will bethe approximate resultant velocity that carries her back to the space station?Astronautmass01 kg-X-Hammermass4 kgoOA. 0.10 m/sB. 0.15 m/sO C. 0.34 m/sOD. 0.05 m/s

Sagot :

ANSWER

B. 0.15 m/s

EXPLANATION

If we consider the system astronaut-hammer as an islotated system and we apply the law of conservation of momentum we have:

[tex]p=0=m_hv_h+m_Av_A[/tex]

Where mh is the mass of the hammer, mA is the mass of the astronaut, vh is the hammer's final velocity and vA is the astronaut's final velocity.

In this system the velocities will be constant, because there are no other forces acting and the initial velocity for both objects is zero (because they are at rest).

Let's solve the equation above for vA:

[tex]v_A=\frac{-m_hv_h}{m_A}[/tex]

The astronaut's velocity is:

[tex]v_A=\frac{-4kg\cdot3.5m/s}{91\operatorname{kg}}\approx-0.15m/s[/tex]

The minus sign indicates that the astronaut is moving in the opposite direction of the hammer's motion. Therefore the correct answer is option B. 0.15m/s

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