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

[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.)

Homework Equations

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

 

[Orodruin]

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?

 

[jybe]

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

 

[TSny]

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.

 

[haruspex]

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.

 

[SammyS]

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:

(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).

 

[TSny]

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:

(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.

 

[SammyS]

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.)

 

[TSny]

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.