A rubber ball is dropped from the top of a hole.Exactly 3.0 seconds later, the sound of the rubber ball hitting bottom is heard.How deep is the hole?
HInt:- The distance that dropped object falls in t sec is represented by the formula s = 16t^2.The speed of sound is 1100 ft/sec
What if the time was 3.5 seconds
Well, let's calculate the distance that the rubber ball fell using the formula s = 16t^2. Given that the time is 3.0 seconds, we can substitute it into the formula:
s = 16(3.0)^2
s = 16(9)
s = 144 feet
So the rubber ball fell 144 feet. Now we need to figure out the depth of the hole using the speed of sound, which is 1100 ft/sec. Since it took 3.0 seconds for the sound to reach your ears, we can multiply the speed of sound by the time:
d = 1100 x 3.0
d = 3300 feet
Therefore, the hole is 3300 feet deep. Wow, that's quite the deep hole! I hope nobody accidentally falls into it while conducting their rubber ball experiments.
To find the depth of the hole, we need to determine the distance that the rubber ball fell in 3.0 seconds.
The formula provided, s = 16t^2, represents the distance an object falls in t seconds. Therefore, plugging in t = 3.0 seconds into the formula, we can calculate the distance fallen by the rubber ball.
s = 16(3.0)^2
s = 16(9)
s = 144 feet
So, the rubber ball fell a distance of 144 feet in 3.0 seconds.
Now, since we know the speed of sound is 1100 ft/sec, we can calculate the time it took for the sound to travel to the top.
Distance = Speed * Time
144 feet = 1100 ft/sec * Time
Solving for Time, we can divide both sides of the equation by 1100 ft/sec:
144 feet / 1100 ft/sec = Time
Time ≈ 0.131 seconds
This means it took approximately 0.131 seconds for the sound to travel from the bottom of the hole to the top.
Finally, we can find the total time it took for the rubber ball to fall and for the sound to travel:
Total time = Time for rubber ball to fall + Time for sound to travel
Total time ≈ 3.0 seconds + 0.131 seconds
Total time ≈ 3.131 seconds
Therefore, the depth of the hole can be calculated by using the formula s = 16t^2, where t = total time. Plugging in t = 3.131 seconds, we can find the depth:
s = 16(3.131)^2
s ≈ 16(9.828361)
s ≈ 157.25376
So, the depth of the hole is approximately 157.25 feet.
If the hole has depth h, then
√h/4 + h/1100 = 3.0
h = 132'8"