A person drops a stone from a bridge. How high is the bridge if they hear the splash 4 seconds later. Assume the speed of sound is 1080ft/sec.
d = 1/2 at^2 = 16t^2
t = sqrt(d)/4
total time = falling time + echo time
4 = sqrt(d)/4 + d/1080
Let s = sqrt(d)
s^2 + 270s - 4320 = 0
s = 15.15
d = 229.52 ft
Check:
falling time = sqrt(229.52/16) = 3.7875
echo time = 229.52/1080 = 0.2125
total: 4 seconds
To determine the height of the bridge, we can use the fact that the time it takes for the stone to hit the water is equal to the time it takes for the sound of the splash to travel back up to the person on the bridge.
First, we need to calculate the time it takes for the stone to hit the water. Since we're given that it takes 4 seconds for the person to hear the splash, we can assume that it also took 4 seconds for the stone to fall. The equation for the time it takes for an object to fall can be calculated using the formula:
time = √(2h/g)
Where:
- time is the time it takes for the object to fall
- h is the height of the object
- g is the acceleration due to gravity, which is approximately 32 ft/sec² on Earth
Rearranging the formula, we can solve for h:
h = (1/2) * g * time²
Plugging in the values, we get:
h = (1/2) * 32 ft/sec² * (4 sec)²
h = 256 ft
So, the height of the bridge is 256 feet.