a ball is released from rest from the twentieth of a building. after , the ball has fallen one such that it is directly outside the nineteenth- window. the are evenly spaced. assume air resistance is negligible. what is the number of the ball would fall in after it is released from the twentieth ?

Problem Restatement

A ball is released from rest from the twentieth floor of a building. After 1 second, it has fallen one floor (so it is just outside the nineteenth-floor window). The floors are evenly spaced. Air resistance is negligible. The question: How many floors will the ball have fallen after 3 seconds?

Step-by-Step Solution

1. Find the distance between floors

• In 1 second, the ball falls one floor.
• For a ball dropped from rest:
  s=12gt2s=\frac{1}{2}gt^2s=21​gt2
  where g=9.8 m/s2g=9.8,\text{m/s}^2g=9.8m/s2, t=1 st=1,\text{s}t=1s.

s1=12×9.8×(1)2=4.9 ms_1=\frac{1}{2}\times 9.8\times (1)^2=4.9,\text{m}s1​=21​×9.8×(1)2=4.9m

So, the height of one floor is 4.9 m. 2. Find the total distance fallen in 3 seconds

s3=12×9.8×(3)2=0.5×9.8×9=44.1 ms_3=\frac{1}{2}\times 9.8\times (3)^2=0.5\times 9.8\times 9=44.1,\text{m}s3​=21​×9.8×(3)2=0.5×9.8×9=44.1m

3. Calculate the number of floors fallen

Number of floors=Total distance fallenHeight per floor=44.14.9=9\text{Number of floors}=\frac{\text{Total distance fallen}}{\text{Height per floor}}=\frac{44.1}{4.9}=9Number of floors=Height per floorTotal distance fallen​=4.944.1​=9

Final Answer

After 3 seconds, the ball will have fallen 9 floors.
So, it will be just outside the 11th-floor window (since it started from the 20th floor and falls 9 floors down).

• This matches with the answer choices found in the referenced sources: the correct range is "7 to 10 floors"

Summary Table

Time after release| Number of floors fallen
---|---
1 s| 1
3 s| 9

Therefore, in 3 seconds, the ball will have fallen 9 floors.