Ga projectile is shot directly away from earth's surface. neglect the rotation of the earth. what multiple of earth's radius re gives the radial distance (from the earth's center) the projectile reaches if (a) its initial speed is 0.216 of the escape speed from earth and (b) its initial kinetic energy is 0.216 of the kinetic energy required to escape earth? (give your answers as unitless numbers.) (c) what is the least initial mechanical energy required at launch if the projectile is to escape earth?

Space-time metric ds2= -dt2+at2dx2+bt2dy2+ct2dz2 (a)how does the area of a rectangle with vertices at ( x=0, y=0, z=0 ), (1,0,0 ), ( 0,1,0 ) and (1,1,0 ) changes with time? (b) if a photon moving in the x direction starts from the origin at t=1, when does it reach x=l? (ds=0 for the trajectory of a photon.) (c) the proper time for a particle is defined by cd=ds. what is the proper time for a particle to move along the trajectory ( x(t)=t, y(t)=0, z(t)=0 ) from t=0 to 1 ? what is the condition on the parameter a so that the velocity of the particle never exceeds the speed of light ?

Several mountains together form a mountain . a few of these combined form a mountain system. several systems combined form a mountain , which can stretch thousands of miles in length.

If gases like carbon dioxide and methane make up less than 1% of the total atmosphere, why is it important for scientists to monitor changes in percentages of these gases?