# Dropping from 4 times the height, how much longer does it take?

We solved this in class 4 months ago but I just can't remember the solution, or even where to start. I remember rearranging an equation. If an object is dropped from a height and it takes T seconds to hit the ground, how long will it take if dropped from four times the height?

A. T seconds.
B. √2 T seconds.
C. 2T seconds.
D. 2 √2 T seconds.
E. 4T seconds.

Can anyone give me a hint without giving the answer?

## Answers and Replies

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Delphi51
Homework Helper
We aren't supposed to help until we see an attempt but just this once I can't resist.
The approach to any problem is to first realize what is going on and write equations that apply to it. In this case, accelerated motion is going on. Can you write equations that apply?

Is it by rearranging s= ut + .5at2?

SammyS
Staff Emeritus
Homework Helper
Gold Member
Is it by rearranging s= ut + .5at2?
Yes, and of course, the initial velocity u is zero.

I keep getting the answer as 2T, is that right? When we did it months ago I'm almost positive it had a root2 in the answer

Dick
Homework Helper
I keep getting the answer as 2T, is that right? When we did it months ago I'm almost positive it had a root2 in the answer
Sure that's right. If the displacement changes by a factor 4, T changes by a factor of 2. You might be thinking of a different problem.

Sure that's right. If the displacement changes by a factor 4, T changes by a factor of 2. You might be thinking of a different problem.
I must be, that's the only thing that was throwing me off since I first saw the question. I thought I remembered a root2 in there so I was doubting the obvious answer of 2T! Anyway, thank you. :)

SammyS
Staff Emeritus
Homework Helper
Gold Member
I keep getting the answer as 2T, is that right? When we did it months ago I'm almost positive it had a root2 in the answer
Yes, 2T is correct.

When the problem was done earlier, in class, was it exactly the same, or just similar. After all, 2=√4 .

Yes, 2T is correct.

When the problem was done earlier, in class, was it exactly the same, or just similar. After all, 2=√4 .
That's true, but for some reason √2 was stuck in my head. At least I know now for incase it comes up in the exam in January, because I would have doubted myself and picked one of the √2 answers.

PeterO
Homework Helper
That's true, but for some reason √2 was stuck in my head. At least I know now for incase it comes up in the exam in January, because I would have doubted myself and picked one of the √2 answers.
When you do the exam in January, are you allowed to take in a self-prepared "formula sheet" or page of notes?

When you do the exam in January, are you allowed to take in a self-prepared "formula sheet" or page of notes?
We are given a formula sheet but I'm not sure if we'e allowed to add anything to it. I planned on finding that out when we go back. Luckily it gives the equations I have the hardest time remembering or being able to prove to myself. I wish we were allowed to take in a page of notes for Algebra... not looking forward to that!