Space probes may be separated from their launchers by exploding bolts. (They bolt away from one another.) Suppose a 4800-kg satellite uses this method to separate from the 1500-kg remains of its launcher, and that 5000 J of kinetic energy is supplied to the two parts. What are their subsequent velocities using the frame of reference in which they were at rest before separation?

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aristocles aristocles · Answer 1 · 2019-12-01T13:09:24+01:00

Answer:

[tex]v_1 = 0.704 m/s[/tex]

[tex]v_2 = 2.25 m/s[/tex]

Explanation:

As we know that the satellite will separate from its remain by using the method of internal energy

So here we can use energy conservation and momentum conservation

so we will have

[tex]m_1v_1 = m_2v_2[/tex]

[tex]4800 v_1 = 1500 v_2[/tex]

[tex]48 v_1 = 15 v_2[/tex]

also by energy equation

[tex]\frac{1}{2}(4800)v_1^2 + \frac{1}{2}1500 v_2^2 = 5000[/tex]

now from above equations

[tex]2400 v_1^2 + 750 v_2^2 = 5000[/tex]

[tex]2400 v_1^2 + 750(\frac{48}{15}v_1)^2 = 5000[/tex]

[tex]10080 v_1^2 = 5000[/tex]

[tex]v_1 = 0.704 m/s[/tex]

[tex]v_2 = 2.25 m/s[/tex]