Question

g 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 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 c and ignoring the effect of air resistance on the balloon, determine how far above the man's ears this point is.

Answer 1

The warning must be shouted before the balloon falls approximately 7.35 meters above the man's ears.

Explanation:

When the water-filled balloon is dropped from a height of 10.0 meters, its potential energy gets converted into kinetic energy as it falls. The equation for potential energy (PE) turning into kinetic energy (KE) is PE = KE. At the point where the potential energy of the balloon becomes equal to the energy produced by the sound wave of the shouted warning, the warning becomes ineffective as the balloon has already passed that point. Using the formula for potential energy, (PE = mgh), where (M) is the mass of the balloon, (g) is the acceleration due to gravity, and (h) is the height.

Setting the potential energy equal to the energy produced by the sound wave (which is related to the intensity and the distance traveled by the sound), we can equate these energies to determine the height at which the warning becomes ineffective. Considering the temperature and neglecting air resistance, the point where the warning would no longer help is approximately 7.35 meters above the man's ears. This implies that for the warning to be effective, it must be shouted before the balloon reaches this particular height.

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Answer 2

The warning will be ineffective if shouted after approximately 1.43 seconds after the balloon is released.

Step-by-step explanation:

To determine the point at which the warning will be ineffective, we need to consider the time it takes for the sound wave to reach the man's ears. The sound wave travels at a speed of approximately 343 m/s in air at 20°C. Since the balloon is released from rest, we can use the equation h = 0.5 * g * t^2, where h is the height of the balloon, g is the acceleration due to gravity (9.8 m/s^2), and t is the time it takes for the balloon to reach the certain point above the man's ears.

Using the equation, we can rearranged it to solve for t:

t = sqrt(2h / g)

Substituting the known values, we have:

t = sqrt(2 * 10.0 / 9.8)

t ≈ 1.43 s

The warning will be ineffective if shouted after approximately 1.43 seconds after the balloon is released.