One-Dimensional Motion Word Problem

[bap902]

Homework Statement

A stone is dropped from a height (h) and falls the last half of its distance in 4 seconds.
(a) What is the total time of the fall?
(b) From what height was the stone dropped?

Homework Equations

h=1/2(g)(T)²

The Attempt at a Solution

T=√2(T-4)

 

[Kurdt]

One will need to set up two equations and most likely divide them to get rid of one of the variables and solve for the other.

 

[baba89]

(a) The total time of the fall can be found by substituting the given values into the equation h=1/2(g)(T)². We know that the stone falls for a total of 4 seconds, so we can plug in 4 for T. We also know that the stone falls for the last half of its distance, so we can plug in 1/2h for h. This gives us the equation 1/2h=1/2(g)(4)². Simplifying, we get h=16g. Therefore, the total time of the fall is 16 seconds.

(b) To find the height from which the stone was dropped, we can use the same equation h=1/2(g)(T)². This time, we know the total time of the fall is 16 seconds, so we can plug in 16 for T. We also know that the stone falls for the last half of its distance, so we can again use 1/2h for h. This gives us the equation 1/2h=1/2(g)(16)². Simplifying, we get h=256g. Therefore, the stone was dropped from a height of 256 meters.