# Calculating Safe Distance for Warning: Flower Pot Falling from 21.6m Height

• jybe
In summary, Homework Equations show that the flower pot can fall 12.5807 meters before it's too late for a warning shouted from the balcony to reach the man in time.
jybe

## Homework Statement

A flower pot is knocked off a window ledge from a height
d = 21.6 m
above the sidewalk as shown in the figure below. It falls toward an unsuspecting man of height
h = 1.71 m
who is standing below. Assume the man below requires 0.300 s to respond to a warning. How close to the sidewalk can the flowerpot fall before it is too late for a warning shouted from the balcony to reach the man in time? (Use 343 m/s for the speed of sound.)

h = 0.5gt^2

## The Attempt at a Solution

Time it takes sound to reach the man = (21.7-1.71)/343 = 0.057988 seconds

Time it takes the flowerpot to reach the man: (21.6-1.71) = (0.5)(9.8)t^2

t = 1.7147 seconds to reach the man

So he needs a warning at (1.7147 - 0.3 - 0.057988) = 1.356712 seconds

h = 0.5(9.8)(1.356712)^2

h = 9.0193 m

(21.6 - 9.0193) = 12.5807 m

So my answer is that it can get 12.5807 m to the sidewalk before it's too late for a warning.

This answer may or may not be correct (I keep getting it wrong, I'm more confident about this time but I don't want to submit it because I have limited attempts). Can anybody verify this for me? Thanks a lot

jybe said:
So my answer is that it can get 12.5807 m to the sidewalk before it's too late for a warning.
Do you think it is reasonable to give sub millimeter precision in your answer given the approximations made and the accuracy in the input data?

Orodruin said:
Do you think it is reasonable to give sub millimeter precision in your answer given the approximations made and the accuracy in the input data?
No

berkeman
jybe said:
Time it takes the flowerpot to reach the man: (21.6-1.71) = (0.5)(9.8)t^2

t = 1.7147 seconds to reach the man
I don't get this value for t when I solve your equation.

Otherwise, I think your overall approach to the problem is good.

TSny said:
I don't get this value for t when I solve your equation.
good catch. Looks like the man's height was taken as 7.11.

TSny
TSny said:
jybe said:
Time it takes the flowerpot to reach the man: (21.6-1.71) = (0.5)(9.8)t^2

t = 1.7147 seconds to reach the man
I don't get this value for t when I solve your equation.

Otherwise, I think your overall approach to the problem is good.
It looks like adding 0.3 seconds to 1.7147 seconds is the value of t obtained as a solution to the above equation.

Edit: Following the post of @TSny below: Ignore the following comment.
DUH !

Also:
jybe said:
(21.6 - 9.0193) = 12.5807 m
It looks like this is the way to find the lowest location (for flower pot) at which a warning will allow the man to prevent the flower pot from smashing his foot (If it misses him otherwise).

Last edited:
SammyS said:
It looks like adding 0.3 seconds to 1.7147 seconds is the value of t obtained as a solution to the above equation.
Yes. So, it appears that the OP ended up subtracting the reaction time of 0.3 s twice, instead of once, when finding the latest time at which the warning can be given.

Also:
jybe said:
(21.6 - 9.0193) = 12.5807 m
It looks like this is the way to find the lowest location (for flower pot) at which a warning will allow the man to prevent the flower pot from smashing his foot (If it misses him otherwise).
I don't see this. It seems to me that once the value of 9.02 m is corrected due to taking into account the reaction time twice, this would give the correct height of the pot above the sidewalk that would allow the man to just prevent the pot from hitting him on the head. But, maybe I'm overlooking something.

TSny said:
Yes. So, it appears that the OP ended up subtracting the reaction time of 0.3 s twice, instead of once, when finding the latest time at which the warning can be given.

I don't see this. It seems to me that once the value of 9.02 m is corrected due to taking into account the reaction time twice, this would give the correct height of the pot above the sidewalk that would allow the man to just prevent the pot from hitting him on the head. But, maybe I'm overlooking something.
Thanks for checking that.

Serious brain CRAMP ! (Maybe it's the spoons.)

SammyS said:
Thanks for checking that.

Serious brain CRAMP ! (Maybe it's the spoons.)
Right. Whenever I wear spoons on my face, I can't think straight.

## What is the formula for calculating safe distance?

The formula for calculating safe distance when a flower pot is falling from a height of 21.6m is: d = √(2gh), where d is the safe distance, g is the acceleration due to gravity (9.8m/s^2), and h is the height of the flower pot.

## At what height should I start calculating the safe distance?

You should start calculating the safe distance from the point where the flower pot is dropped, which in this case is 21.6m. This is the initial height from which the flower pot will fall.

## What units should the final answer be in?

The final answer should be in meters (m) as it represents the distance from the point of impact where the flower pot will fall.

## What is the purpose of calculating the safe distance?

The purpose of calculating the safe distance is to determine the minimum distance that people or objects should be from the point of impact in order to avoid potential harm or damage from the falling flower pot.

## Is there any other factor that should be considered when calculating the safe distance?

Yes, in addition to the height of the flower pot and the acceleration due to gravity, other factors such as air resistance, wind speed, and the size and weight of the flower pot can also affect the safe distance and should be taken into consideration when making the calculation.

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