Little Milly/Willy/Time and Height

[rpullo]

Homework Statement

Little Willy, clumsy clot,
From window sill dislodged a pot.
He shouts below to Little Milly:
"Step aside, it'll knock you silly!"

The window sill is 35.0 m above the sidewalk where Millly is standing directly below the falling pot. Milly is 1.05 m tall, her ears are 5.00 cm below the top of her head, and she needs 0.400 s to respond to the warning. The speed of sound in air is 340 m/s. What is the minimum height of the pot above the ground at the instant Willy shots his warning if Milly is to avoid being "potted"? Answer in m.

Homework Equations

v =d/t
d = (v1)t + 0.5a(t^2)

The Attempt at a Solution

So I first found the time is takes for the sound to reach Milly's ears:

t = d/v
t = (35.0m - 1.0m)/(340m/s)
t = 0.10 s

So the time it takes Milly to receive the warning and respond:

0.10 s + 0.400 s = 0.50 s

I use d = (v1)t + 0.5a(t^2) to find the distance the pot falls:

d = (v1)t + 0.5a(t^2) ...where v1 is 0
d = 0.5(-9.8)(0.50)^2
d = 1.225 m

I'm not sure what to do next or if I even started this question correctly. All input is appreciated!

 

[rpullo]

Alright, scratch the top part. I've thought of this as a solution and was wondering if anyone can confirm this.

i. Time is takes for the sound to reach Milly:

t = d/v = (35.0 m - 1.0 m)/340 m/s = 0.10s

ii. Time is takes for warning to reach Milly and for her to respond:

0.10 s + 0.400 s = 0.50 s

iii. Time it takes the pot to hit Milly's head:

d = 33.95 m; v₁ = 0; a = 9.80 m/s²

d = v₁t + 0.5at²
33.95 = (0.5)(9.80)t²
t = 2.63 s

Time Willy needs to warn Milly:

2.63 s - 0.50 s = 2.13s

Distance the pot will fall:

t = 2.13 m; v₁ = 0; a = 9.80 m/s²

d = v₁t + 0.5at²
d = 0.5(9.80)(2.13)²
d = 22.28 m

Height of the pot above the ground:

35.0 m - 22.28 m = 12.7 m

 

[denverdoc]

looks good.