# When calculating escape speed why is v_f =0

1. Sep 30, 2007

That's all. I am just trying to derive the reason why when using comservation of mechanical energy $$v_{final}$$ goes to zero?

2. Sep 30, 2007

### Staff: Mentor

The escape speed is the minimum speed to just barely make it to infinity with no energy left. So the final speed is zero.

3. Sep 30, 2007

### jedisoccer

Last edited: Sep 30, 2007
4. Sep 30, 2007

### AbedeuS

Because escape speed is the minimum velocity at distance $$r=x$$ that the object has to be moving in order to break away from the gravitational pull of a planet at a velocity of 0.

As the object moving at speed $$V_{initial}$$ moves from $$r = x$$ to $$r=\frac{1}{0}$$ the force of earths gravity decellerated the object (use equation: $$F=ma$$) and this causes the object to, of course, lose speed, the escape velocity therefore is a velocity that puts you JUST out of reach of a planets gravitational field, but fully decellerated, moving faster than the escape velocity will mean that you will have additional, yet reduced speed after escaping the gravitational field.

5. Sep 30, 2007