Question

two coconuts fall freely from the rest at the same time, one from a tree twice as high as the other. If the coconut from the shorter tree takes 2.0s to reach the ground, how long will it take the other coconut to reach the ground

Answer 1

since the value of g is constent so when hight is doubled time period will also be doubled

Answer 2

Acceleration is (approximately) g in both cases.

Distance above ground is h - 0.5*g*t^2 for the lower coconut.

We are given that h - 0.5*g*(2)^2 = 0, thus h = 2g ~ 20 meters.

We know that the other higher coconut is 2*h = 4g ~ 40 meters above the ground. Can you finish it from here?

Answer 3

@leon549
That is not a correct answer.

The time would be doubled IF the VELOCITY of the two coconuts was the same and constant.
HOWEVER
You can see that when the higher nut reaches the height of the lower one IT IS TRAVELLING at a significant speed, whereas the lower one starts from REST at this point.

The higher on therefore covers the lower HALF in less time than the lower one does.

if h is lower height and t1 is time for lower nut to fall

then the equation is
h = 0.5g (t1)^2

if H is upper height and t2 is time for upper nut to fall

then the equation is
H = 0.5g (t2)^2

BUT H = 2h

so you can solve for t2