Aprojectile of mass m is fired straight upward from the surface of an airless planet of radius r and mass m with an initial speed equal to the escape speed vesc (meaning the projectile will just barely escape the planet's gravity -- it will asymptotically approach infinite distance and zero speed.) what is the correct expression for the projectile's kinetic energy when it is a distance 9r from the planet's center (8r from the surface). ignore the gravity of the sun and other astronomical bodies. ke (at r = 9r) is: a. gmm/9rb. gmm/8rc. 1/2mvesc^2d. -gmm/8re. none of these

K = G Mm / 9R

Explanation:

Expression for escape velocity V_e =

Kinetic energy at the surface = 1/2 m V_e ²

= 1/2 x m x 2GM/R

GMm/R

Potential energy at the surface

= - GMm/R

Total energy = 0

At height 9R ( 8R from the surface )

potential energy

= - G Mm / 9R

Kinetic energy = K

Total energy will be zero according to law of conservation of mechanical energy

so

K  - G Mm / 9R = 0

K = G Mm / 9R

b. latent learning (the word "latent" itself means something that exists but isn't obvious, only under certain conditions! )

c. 7/3

step-by-step explanation:

a rational number is like pi- it is a repeating decimal.

a. is -1.8

b. 2.236068

c. 2.3333333333333333333

d.   is 3

i hope that ! =)