Question

the escape velocity from earth is Ves.a body is projected with velocity 2Ves with constant velocity will it move in the interplanetary space​

Answer 1

Answer:

$ves\sqrt{3}$

Explanation:

Refer to the material.

Answer 2

Answer:

The velocity is $\sqrt{3} \ v_{es}$ to move in interplanetary space.

Explanation:

According to the question,

the body moves with constant velocity in interplanetary space.

From conservation of energy,

                            $\frac{1}{2} m v_{p}^2 -\frac{GMm}{R} = \frac{1}{2} m v^2 + 0$     [ $v_{p}$ → Projected velocity]

                      →      $v^{2} = v_{p} ^2 - \frac{2GM}{R}$        

                      →     $v^{2} = v_{p} ^2 - v_{es} ^2$                    [ Escape Velocity, $v_{es} = \sqrt \frac{2GM}{R}$ ]

                      →    $v = \sqrt{ v_{p} ^2 - v_{es} ^2$  

                      →   $v =\sqrt{ (2v_{es} )^2 - v_{es} ^2$               $[ v_{p} = 2 v_{es} ]$

                               $= \sqrt{3v_{es}^2 }$ $= \sqrt{3}\ v_{es} }$  [Ans]