A particle is fired vertically upwards with a speed of 15 $k m / s$ . With what speed (in $k m / s$ ) will it move in interstellar space? Assume only earth’s gravitational field.

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Solution

space in which our sun effect is neglible is called interstellar space.
By conservation of mechanical energy,
$\frac{- G M m}{R} + \frac{m v_{0}^{2}}{2} = \frac{m v^{2}}{2}$
$\frac{- G M}{R} + \frac{v_{0}^{2}}{2} = \frac{v^{2}}{2}$
Substituting the values,
$G = 6.67 \times 10^{- 11}, M = 6 \times 10^{24} k g, R = 6400 k m, v_{0} = 15 k m s^{- 1}$
$v = 10 k m s^{- 1}$

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A particle is fired vertically upwards with a speed of 15 km/s. With what speed (in km/s) will it move in interstellar space? Assume only earth’s gravitational field.

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A particle is fired vertically upwards with a speed of 15 $k m / s$ . With what speed (in $k m / s$ ) will it move in interstellar space? Assume only earth’s gravitational field.