Calculating Free Fall: Water Balloon Question | Math Homework Help

[hershey1]

Homework Statement

A student at a window on the second floor of a dorm sees his math professor walking on the sidewalk beside the building. He drops a water balloon from 18.0 m above the ground when the prof is 1.00 m from the point directly beneath the window. The professor is 170 cm tall and walks at a rate of 0.450 m/s. How close does the balloon come to hitting the professor?

Homework Equations

y=v0t + 1/2gt^2

The Attempt at a Solution

I found the displacement to be 16.3 m from subtracting the distance of the building from the man's height. Using the formula, I calculated the time to be 3.3 seconds. This would say that the prof will not be hit by the water balloon since the prof would have walked only 82 cm by then. My answer was 18 cm but it was wrong.

 

[Hootenanny]

Homework Statement

A student at a window on the second floor of a dorm sees his math professor walking on the sidewalk beside the building. He drops a water balloon from 18.0 m above the ground when the prof is 1.00 m from the point directly beneath the window. The professor is 170 cm tall and walks at a rate of 0.450 m/s. How close does the balloon come to hitting the professor?

Homework Equations

y=v0t + 1/2gt^2

The Attempt at a Solution

I found the displacement to be 16.3 m from subtracting the distance of the building from the man's height. Using the formula, I calculated the time to be 0.82 seconds. This would say that the prof will not be hit by the water balloon. My answer was 18 cm but it was wrong.

Welcome to PF hershey1,

You may want to recheck your calculation of the flight time.

 

[baba89]

I would like to clarify that the calculation for the time of the water balloon's fall is correct, but the distance the professor walks in that time is incorrect. The professor walks at a rate of 0.450 m/s, so in 3.3 seconds, he would have walked a distance of 1.485 m, which is significantly more than the 82 cm calculated. Therefore, the water balloon would come closer to hitting the professor than initially thought. To determine the exact distance, we would need to use the equation for horizontal displacement, x=v0t, where x is the horizontal distance, v0 is the initial velocity (which in this case is 0), and t is the time. This would give us a horizontal displacement of 1.485 m. We can then use the Pythagorean theorem to find the distance between the balloon and the professor, which would be approximately 16.4 m. Therefore, the balloon would come within approximately 16.4 m of hitting the professor.