Just for fun, a person jumps from rest from the top of a tall cliff overlooking a lake. in falling through a distance h, she acquires a certain speed v. assuming free-fall conditions, how much farther must she fall in order to acquire a speed of 2v? express your answer in terms of h.
b. would the answer to part
a. be different if this event were to occur on another planet where the acceleration due to gravity had a value other than 9.80 m/s2? explain.

For this we need to use several formulas:
v = a*t
This simply means that after 1 second we will have some speed and if we double time, speed will double as well.

But, relation time-traveled distance isn't linear. Traveled distance we calculate:
s = 1/2*a*t^2                we can say that h=s
so if we double time, traveled distance will increase 4 times because of square relation between time and traveled distance.

New traveled distance (h2) will be: h2=4*h

b)  Because distance depends on gravity acceleration in free fall h2 will certainly change but the relation h2=4*h will remain the same.