A student at a window on the second floor of a dorm sees his moth professor walking on the sidewalk beside the builiding. he drops a water ballon from 18.0 meters above the ground when the professor is 1.00 meters from the point directly beneath the window. if the professor is 170 cm tall and walks at a rate of .450 m/s, does the balloon hit her? if not, how close does it come?

Question

A student at a window on the second floor of a dorm sees his moth professor walking on the sidewalk beside the builiding. he drops a water ballon from 18.0 meters above the ground when the professor is 1.00 meters from the point directly beneath the window. if the professor is 170 cm tall and walks at a rate of .450 m/s, does the balloon hit her? if not, how close does it come?

Answer 1

To determine whether the water balloon hits the professor, we need to calculate the time it takes for the professor to reach the point directly beneath the window and compare it with the time it takes for the water balloon to fall from the window to the ground.

Let's break down the problem step by step:

1. Find the time it takes for the professor to reach the point directly beneath the window:
Distance = Velocity x Time
Time = Distance / Velocity
Given that the professor is 1.00 meter away from the point directly beneath the window and walks with a velocity of 0.450 m/s:
Time = 1.00 m / 0.450 m/s = 2.22 seconds (rounded to two decimal places)

2. Calculate how far the professor moves during the time it takes for the water balloon to fall:
Distance = Velocity x Time
Given that the professor walks at a rate of 0.450 m/s and the calculated time is 2.22 seconds:
Distance = 0.450 m/s x 2.22 s = 0.999 meters (rounded to three decimal places)

3. Determine whether the balloon hits the professor:
Since the professor is 170 cm tall (or 1.70 meters), and the balloon is dropped 18.0 meters above the ground, the balloon will hit the professor if the distance it falls is less than the distance the professor moves.
Comparing the distance the balloon falls (18.0 meters) with the distance the professor moves (0.999 meters), we can see that the balloon will not hit the professor because the balloon's distance is greater.

4. Calculate how close the balloon comes to hitting the professor:
To determine how close the balloon comes to hitting the professor, we subtract the distance the professor moves from the distance the balloon falls:
Closest distance = Distance the balloon falls - Distance the professor moves
Closest distance = 18.0 m - 0.999 m = 17.001 meters (rounded to three decimal places)

Therefore, the water balloon does not hit the professor but comes closest to her at a distance of 17.001 meters.