Saturday

October 25, 2014

October 25, 2014

Posted by **Jessy** on Monday, January 15, 2007 at 11:29am.

(a) As a multiple of Earth's radius RE, what is the radial distance a projectile reaches if its initial speed is one-fifth of the escape speed from Earth?

____ times RE

(b) As a multiple of Earth's radius RE, what is the radial distance a projectile reaches if its initial kinetic energy is one-fourth of the kinetic energy required to escape Earth?

_____ timesRE

(c) What is the least initial mechanical energy required at launch if the projectile is to escape Earth?

These problems all can be solved by using the Conservation of Energy relationship

Total Energy = KE + PE =

(1/2) m V^2 - GMm/R = constant

wher M is the mass of the earth, m is the mass of the projectile and R is the distance from the center of the Earth.

The "escape speed" Ve is the launch velocity that allows V to be zero when R = infinity. Thus

(1/2) m Ve^2 - G M m/Re = constant

Ve = sqrt (2 G M/Re)

Here is how to do (a):

If V = (1/5) Ve at R = Re, then

(1/2) m V^2 - G M m/R = constant

= (1/50) m Ve^2 - G M m/Re

When V = 0 (maximum value of R),

(1/50) Ve^2 = GM [(1/Re - (1/R)]

(1/25) G M/Re = G M [(1/Re - (1/R)]

GM/R = (24/25)(GM/Re)

R/Re = 25/24

Proceeds imilarly for (b)

For (c), the least mechanical energy (including potential energy), is zero, since potential energy is defined as zero at infinite distance, as is almost always done in inverse-square law situations. This is the case when PE = - G M m/R

Your explanaion is very clear to me. Thank you.

- Physics Question......many thanks -
**Max**, Tuesday, November 9, 2010 at 11:35pmSorry, your explanation made too many logical leaps. How did you get from 1/5 to 1/50??? It's garbage like this that makes you want to never see physics problems again.

- Physics Question......many thanks -
**Jon**, Saturday, November 20, 2010 at 1:08amAmen Max!

- Physics Question......many thanks -
**.**, Thursday, March 31, 2011 at 11:21pm1/2(1/5Ve)^2 = 1/2 * 1/25 * Ve^2 = 1/50Ve^2

- Physics Question......many thanks -
**edward**, Wednesday, June 18, 2014 at 9:40amwhy is it 1/50??

**Answer this Question**

**Related Questions**

Gravitation help..........thanks - A projectile is shot directly away from Earth...

physics - The earth has a radius of 6380 km and turns around once on its axis in...

Physics - Neglect the gravity of the Moon, neglect atmospheric friction, and ...

Physics - At the heighest point on earth, the distance to the center of the ...

Physics - PROJECTILE LAUNCHED FROM EARTH'S SURFACE? A projectile is shot ...

Physics - A projectile is fired vertically from Earth's surface with an initial ...

PHYSICS(HELP!!) - A hole is drilled with smooth sides straight through the ...

physics help (elena) - A hole is drilled with smooth sides straight through the ...

physics (PLS HELP) - A hole is drilled with smooth sides straight through the ...

physics - A hole is drilled with smooth sides straight through the center of the...