A 5m tall elevator travels uniformly up an elevator shaft at 8 m/s. At some point in time, a bolt falls from the top of the elevator and falls freely down the shaft. You can ignore the effect of air resistance.

a) How many seconds after the fall will the bolt pass the bottom of the elevator?

b) Now assume that the bolt falls from the *wall* of the elevator shaft, and then falls freely without air resistance. How many seconds after the fall will the bolt pass the bottom of the elevator?

For the first question (a), I was able to solve the problem... See:

I made a draw to understand the "dynamics" of the environment and computed the Xf for the elevator and bolt:

Xfb = Xib + Vit + 1/2 at^2

= 0 - 8t + 9.8/2 t^2

Xfb = 4.9t^2 -8t

Xfe = 5 - 8t (constant speed)...

Then, by equaling them:

5 -8t = 4.9t^2 -8t

5 = 4.9t^2

5/4.9 = t^2

t = sqrt(1.02) = 1.01 ;

Now... for the b question, I'm really struggling in relating the distance between the bolt and elevator.... I tried to mount the equations based on the bolt frame:

Xfb = h + 0t + 9.8/2 t^2 (considering initial position at the elevator floor)...

Xfe = Xi - 8t;

I'm trying to relate the initial position of the elevator to h of the bolt... But, so far, no good... =/ ...

Could someone, please, bring me some light to this problem?