A ball is dropped into a well. A splash is heard 43 seconds later. The speed of sound (the speed at which sound travels through the air) is 345 m/s.
HOW DEEP WAS THE WELL?
I don't even know which equation to plug this into. At first I just tried s=d/t-> 345=d/43, but that gave me a value that was too big/ incorrect. What should I do?
During fall, it is under the influence of gravity
d=4.9 t^2 where t is the time it fell.
t= sqrt d/4.9
not sound has to go back up.
d=345*t1 where t1 is the time back up.
but you ARE given t+t1=43 seconds (deep well)
so,
43=t+t1=d/343 + sqrt (d/4.9)
solve this quadratic equation for d Hint, let d= 4.9^2 x^2
To determine the depth of the well, you need to consider both the time it takes for the sound to travel up from the bottom of the well and the time it takes for the ball to fall from the top of the well to the water level.
Let's break it down step by step:
1. Calculate the time it takes for the sound to travel up from the bottom of the well. Since the sound travels at a speed of 345 m/s and it takes 43 seconds to hear the splash, you can use the equation:
distance = speed × time
distance = 345 m/s × 43 s
distance = 14835 meters (rounded to the nearest meter)
2. Now, consider the time it takes for the ball to fall from the top of the well to the water level. Since the ball is dropped, we need to use the equations of motion to calculate the time. The equation that relates time, distance, and acceleration due to gravity for a falling object is:
distance = 0.5 × g × t²
where g is the acceleration due to gravity (approximately 9.8 m/s²) and t is the time.
In this case, the distance is the depth of the well (d) that we are trying to find and the time is unknown. Rearrange the equation to solve for t:
t = √(2d / g)
3. Substitute the value of time (t) calculated from the sound's travel time into the equation derived from the ball's falling time:
√(2d / g) = 43 seconds
4. Square both sides of the equation to isolate the depth (d):
2d / g = 43²
5. Solve for d:
d = (43² × g) / 2
6. Substitute the value of g (approximately 9.8 m/s²) and calculate:
d ≈ (43² × 9.8 m/s²) / 2
d ≈ 8937 meters (rounded to the nearest meter)
Therefore, the depth of the well is approximately 8937 meters.