# Limits and Free Falling Objects

1. Sep 28, 2008

### pippintook

Use the position function s(t)=-49t^(2) + 200 which gives the height of an object that has fallen from a height of 200 meters. The velocity at time t = a seconds is given by the limit as t goes to a = (s(a) - s(t))/(a-t).
At what velocity will the object impact the ground?

I used V^2 = 2gh and got 62.6 m/s, but am not sure if that is right or if there is another formula I should use.

2. Sep 28, 2008

### gabbagabbahey

The question asks you to find $v(a)$ by computing the limit,

$$\lim_{t \to a} \frac{s(a)-s(t)}{a-t}$$

not by plugging it into a kinematics formula.

$v(a)$ is the instantaneous speed of the object at the time $t=a$. The V you just found is different; it is the speed of the object the instant before it hits the ground, not the speed at t=a. Try your hand at the limit above.

Last edited: Sep 28, 2008