00:01
In the first part of a question we've been asked on how high can one jump from a standing start on earth.
00:07
Now let the height from which we can jump be taken as h.
00:17
Then the rays in gravitational potential energy will be given as m g h.
00:25
Now by conservation of energy we know that the kinetic energy of the particle at the start of the jump jump must be equal to the potential energy at height h.
00:56
Substituting the formula is we have half mv square equating m g h, which gives us after rearranging the speed of the particle to be equal to 2 j h.
01:09
This is how we will be able to determine the speed when we jump from a starting point on earth.
01:16
In the next case we are told that a typical asteroid has a density or 2 ,500 kg meter cube.
01:25
Using our result from the previous part we need to estimate the radius of the largest asteroid from which we could reach escape speed just by jumping.
01:34
Now let the radius of the asteroid be r.
01:45
Now we know that mass is equivalent to density into volume.
01:51
Substitating the volume of density being 2500 kg meter cube and volume being 4 pi by 3 are the whole cube.
02:03
Now the gravitational energy at the surface will be given as g m2 by r where m1 is the mass of the asteroid and m2 is the mass of the body.
02:27
Substituting respective values we have g multiplied by 2500 into 4 by 3 by r the whole cube m by r equal to half m v square...