# Little Milly/Willy/Time and Height

• rpullo
In summary, the minimum height of the pot above the ground at the instant Willy shouts his warning for Milly to avoid being "potted" is 12.7 m.
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!

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

looks good.

## 1. What is "Little Milly/Willy/Time and Height"?

"Little Milly/Willy/Time and Height" is a scientific experiment that involves dropping a small object, such as a tennis ball or a toy car, from a height and measuring the time it takes for the object to reach the ground.

## 2. What is the purpose of the "Little Milly/Willy/Time and Height" experiment?

The purpose of this experiment is to demonstrate the relationship between time and height, as well as the effects of gravity on falling objects. This experiment can also be used to calculate the acceleration due to gravity.

## 3. How do you conduct the "Little Milly/Willy/Time and Height" experiment?

To conduct this experiment, you will need a stopwatch, a small object, and a tall structure, such as a building or a ladder. Start the stopwatch as you drop the object from the top of the structure and stop it as the object hits the ground. Repeat this process multiple times and record your results.

## 4. What factors can affect the results of the "Little Milly/Willy/Time and Height" experiment?

The results of this experiment can be affected by factors such as air resistance, wind, and the shape and weight of the object being dropped. To ensure accurate results, it is important to conduct the experiment in a controlled environment and use the same object for each trial.

## 5. How can the data from the "Little Milly/Willy/Time and Height" experiment be used in real-life applications?

The data collected from this experiment can be used to understand and predict the motion of falling objects, which has practical applications in fields such as engineering and physics. It can also be used to teach the concepts of gravity and acceleration to students in a hands-on and interactive way.

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