Discussion question from university physics

[hagglebaby]

Homework Statement

When you drop an object from a certain height, it takes time T to reach the ground with no air resistance. If you dropped it from 3 times that height, how long (in terms of T) would it take to reach to the ground?

Homework Equations

displacement=V₀t+.5g(t)²

The Attempt at a Solution

i got T=sqrt2 and T=sqrt6 but now I'm stuck on how to set up the next proportion. Also would like to see how you started this one.

 

[PeterO]

Homework Statement

When you drop an object from a certain height, it takes time T to reach the ground with no air resistance. If you dropped it from 3 times that height, how long (in terms of T) would it take to reach to the ground?

Homework Equations

displacement=V₀t+.5g(t)²

The Attempt at a Solution

i got T=sqrt2 and T=sqrt6 but now I'm stuck on how to set up the next proportion. Also would like to see how you started this one.

Perhaps you could consider the case of dropping a mass , on Earth where g = 9.8, from a height of 1 m and 3 m then 8 m and 24 m and see if that gives you any hints.

 

[hagglebaby]

thank you! I think the answer is sqrt3