As a prank, someone drops a water-filled balloon out of a...

As a prank, someone drops a water-filled balloon out of a window. The balloon is released from rest at a height of $10.0 \mathrm{~m}$ above the ears of a man who is the target. Then, because of a guilty conscience, the prankster shouts a warning after the balloon is released. The warning will do no good, however, if shouted after the balloon reaches a certain point, even if the man could react infinitely quickly. Assuming that the air temperature is $20^{\circ} \mathrm{C}$ and ignoring the effect of air resistance on the balloon, determine how far above the man's ears this point is.

Key Concepts

Free?Fall Kinematics

This concept involves analyzing the motion of an object that is falling solely under the influence of gravity. The key relationship is that the distance fallen is proportional to the square of the elapsed time (d = ½ g t²), which allows one to compute the fall time from a given height in the absence of air resistance.

Gravitational Acceleration

Gravitational acceleration (denoted by g) is the constant rate at which all objects accelerate downwards near the Earth’s surface when air resistance is negligible. It is pivotal in calculating how quickly an object falls from a specific height.

Speed of Sound in Air

The speed of sound is the rate at which sound waves travel through a medium such as air and depends on factors like temperature. At around 20°C, the speed of sound is approximately 343 m/s. This value is essential when determining how long it takes for a sound (such as a warning shout) to travel a given distance.

Signal Propagation Delay

Even if a person could react instantaneously upon receiving a warning, the finite speed of the warning signal (sound) means there is a delay between the time the warning is issued and when it is heard. This delay—calculated by dividing the distance the sound must cover by the speed of sound—is crucial in scenarios where timing is critical, such as avoiding a fast?arriving object.

Transcript

00:01 In this problem, we have to kill claire.

00:02 The distance from the boyd where the balance reach when the men heard the warning to the man's head.

00:11 We call this distance edge what's right then.

00:15 Expression to kill.

00:16 Clear the time taken by the sun with three demands, it equals to wonder.

00:22 Why didn't we? here actually is the distance from the window.

00:28 Two.

00:28 The men sit and with the speed of sound by setting the weather's into this equation, we can right? do you close to 10.0 mentor divided by 343 meter per second, which is equal to 0.292 seconds.

00:46 No luck.

00:47 Skill.

00:47 Create the final speed off the bed battle through the expression to gh want opposed to.

00:55 We have square minus.

00:56 We're square now it's holding this quitting for we have weakened white.

01:01 We have vehicles to square door to the edge.

01:05 This is a great number one.

01:07 Please know that battle is torn from the rest.

01:10 So we said it this week.

01:12 Isaac wants to zero.

01:14 This is equal to zero now.

01:19 Setting the weather's into this acquaint we will get...