A water balloon is dropped from a cliff. Exactly 3 sec later, the sound of the balloon hitting the ground reaches the top of the cliff. How high is the cliff? (Thanks in advance for any help you can provide!)
height = -4.9t^2
when t = 3
height = 4.9(9) m = appr 44.1 m
If you want to include the travel time of the sound, you have to look up the speed of sound in air. Let's say that is 343.2 m/s. So now, if the falling time is t, then we have
4.9t^2 = 343.2(3-t)
t = 2.88
So, the balloon fell for only 2.88 seconds, making the distance
4.9*2.88^2 = 40.64 m
Well, thank you for the question and for raising my spirits! Now, let's tackle this tall task together.
We can use the equation d = 0.5gt^2, where d is the height of the cliff, g is the acceleration due to gravity (approximately 9.8 m/s²), and t is the time taken for the sound to reach the top.
Given that it took 3 seconds for the sound to reach the top, we'll plug that into our formula:
d = 0.5 * 9.8 * (3^2)
d = 0.5 * 9.8 * 9
d ≈ 44.1 meters
So, based on my calculations, it seems the cliff is approximately 44.1 meters high. However, keep in mind that this doesn't account for air resistance, sound speed, or variations in gravitational acceleration, which can all slightly affect the result.
I hope that helps and brings a smile to your face!
To determine the height of the cliff, we can use the equation of motion under constant acceleration. The key piece of information is the time it takes for the sound of the balloon hitting the ground to reach the top of the cliff, which is given as 3 seconds.
The equation we will be using is:
h = (1/2) * g * t^2
Where:
h is the height of the cliff
g is the acceleration due to gravity (9.8 m/s^2 on Earth)
t is the time it takes for the sound to reach the top of the cliff (3 seconds in this case)
Plugging in the values:
h = (1/2) * (9.8 m/s^2) * (3 s)^2
h = (1/2) * (9.8 m/s^2) * 9 s^2
h = 44.1 meters
Therefore, the height of the cliff is approximately 44.1 meters.