A rock is dropped from a sea cliff and the sound of it striking the ocean is heard 3.9 s later. If the speed of sound is 340 m/s, how high is the cliff?
i know you use the equation y=(initial velocity)(time) + (1/2)(acceleration)(time^2) but I'm having problems putting all the pieces together. If someone could walk me through the steps I would be very grateful.
Certainly! To solve this problem, you need to consider two components: the time it takes for the rock to fall and the time it takes for the sound to reach your ears.
First, let's find the time it takes for the rock to fall. We know that the acceleration due to gravity is approximately 9.8 m/s^2, and we can assume the rock is dropped, so the initial velocity is 0 m/s. We'll use the equation you mentioned:
y = (initial velocity)(time) + (1/2)(acceleration)(time^2)
Since the initial velocity is 0, the equation simplifies to:
y = (1/2)(acceleration)(time^2)
y = (1/2)(9.8)(time^2)
y = 4.9(time^2)
Now let's find the time it takes for the sound to reach your ears. We are given that the speed of sound is 340 m/s, and the time it takes for the sound to be heard is 3.9 seconds.
To find the distance traveled by sound, we'll use the formula:
Distance = Speed x Time
Distance = 340 x 3.9
Now we have the distance traveled by sound, but we need to find the distance the rock has traveled. Since sound and the rock travel simultaneously, the distance is the same for both.
Finally, we can equate the distance traveled by the rock to the distance traveled by the sound:
4.9(time^2) = 340 x 3.9
Now you can solve for time by rearranging the equation:
time^2 = (340 x 3.9) / 4.9
time^2 = 271.02
time ≈ 16.47 seconds
We now have the time it takes for the rock to fall. Substituting this value back into the equation, we can solve for the height of the cliff:
y = 4.9 x (16.47)^2
Calculating this equation will give you the height of the cliff.