Free fall and one other question

[wonger]

So i have two questions i need help answering. its not homework, but its from a previous exam my teacher gave.

x0=x knot and v0= v knot

Homework Statement

a rock dropped from a cliff falls one-third of its total distance to the ground in the last second of its fall. determine the height of the cliff

Homework Equations

v=v0+at
x=x0+v0+.5at^2
i don't think any of the other kinetic equations are relevant

The Attempt at a Solution

i know that the equation for the last second of freefall is x=x0+v0-4.9(1)^2 and v= v0-9.8.

im not sure where to start here. my first impression is that i have to find the final velocity before it hits the ground, but I am not sure what to do to find it.

second question

Homework Statement

a train pulls away from a station with a constant a cceleration of .4 m/s^2. a passenger arrives at the track 6.0s after the end of the rtain has passed the very same point. what is the slowest constant speed at which she can run and catch the train?

Homework Equations

v=v0+at
x=x0+v0+.5at^2
v^2=v0^2+2a(xf-x0)

The Attempt at a Solution

@6seconds, its position is 7.2m from starting point and its velocity is 2.4 m/s. I am not exactly sure what to do on this one either, i know that you have to "optimize" the problem by setting them equal to each other, but I am not really sure which equations to use cus any equation i use i get two variables.

 

[rl.bhat]

Hi wonger, welcome to PF.
Height of the cliff x = 0.5*g*t^2 ...(1)
Distance traveled in (t-1) s is
x1 = 0.5*g*(t-1)^2...(2)
In the problem it is given that
x - x1 = x/3. From these hints find t and then x.