Physics, asked by rawatsushma095, 1 year ago

rocket is fired with speed V = 2 under root gr , directed upward find its speed in interstellar space​

Answers

Answered by suskumari135
1

Speed of rocket in interstellar space is \bf{\sqrt{2gR}}

Explanation:

Given that,

A rocket is fired with a velocity V = 2\sqrt {gR}  near the earths surface and goes upwards

Let us consider ,v be the speed of rocket in interstellar space.

In interstellar space, gravitational potential energy is zero

Applying conservation of energy at surface and interstellar space:

We know that

= \frac{1}{2}m(2( \sqrt {gR}\;)^2

= \frac{1}{2}mv_e^2 + \frac{1}{2}mv^2

= \frac{1}{2}m( \sqrt {2gR})^2 + \frac{1}{2}mv^2

\frac{1}{2}mv^2 = \frac{1}{2}m(2 \sqrt {gR}\;)^2 - \frac{1}{2}m( \sqrt {2gR}\;)^2

v^2 = (2\sqrt{gR})^2- (\sqrt{2gR})^2 = 4gR - 2gR =2gR

v= \sqrt{2gR}

Thus, speed of rocket in interstellar space is \bf{\sqrt{2gR}}

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