What is the escape speed of a projectile fired from Earth's surface at 8.2 km/s?

[CinderBlockFist]

A projectile if fired vertically from Earth's surface with an initial speed of 8.2 km/s. Neglecting air drag, how far from the survace of Earth will it go?


Well, I know that the escape speed of Earth is 11.2 km/s. how would i go about solving this?

 

[learningphysics]

It's not really an escape speed problem... Are you supposed to use the escape speed of the Earth to solve it?

I'd use conservation of energy methods to solve it...

 

[vincentchan]

use conservation of energy... your final velocity is 0...
the potential energy might a little bit tricky for you... just remind you... PE=mgh doesn't work in this case

PS. flying at 8.2km/s on the Earth and ignore the air drag? that is so not realistic..

 

[CinderBlockFist]

crap, i am looking at the formula y - yo = voysin(thetao) - gt, i don't know how to put it in this equation, can someone help me?

 

[clive]

As vincentcahn told you before, you can't use the laws of motion in uniform gravitational field, because the projectil will go far away from the Earth' surface.

Use
$$E_p=-\gamma \frac{mM}{R+h}$$
for the potential energy
and
$$E_c=\frac{mv^2}{2}$$
for the kinetic one and apply the conservation of total energy.

 

[CinderBlockFist]

ahhh, ok thanks clive!