two rocks are dropped off a cliff. the second rock hits 1.6 s after the first. how far below the cliff is the second stone when the rocks are 36m apart? (10.97m)
You have only provided one bit of information, but there are two independent or unspecified variables: the height of the cliff and the delay between the times of release. Without more information, there is no unique solution. There may be an infinite number of possible solutions.
To find the distance below the cliff at which the second rock is located, given the time delay and the distance between the rocks, we can use the equations of motion for free-falling objects.
Let's denote the distance below the cliff at which the second rock is located as "d" and the time it takes for the first rock to hit the ground as "t". We are given that the time delay between the rocks is 1.6 seconds (t = 1.6 s) and the distance between the rocks is 36 meters.
First, we'll find the time it takes for the second rock to hit the ground. Since the second rock is dropped 1.6 seconds after the first rock, the time it takes for the second rock to hit the ground will be the sum of the time it takes for the first rock to hit the ground (t) and the time delay (1.6 seconds). So, the total time for the second rock to hit the ground is t + 1.6 seconds.
The equation for the distance covered by a free-falling object is given by:
d = (1/2) * g * t^2
where "g" is the acceleration due to gravity (approximately 9.8 m/s^2).
Using this equation, we can find the distance covered by the first rock (d1), which took t seconds to hit the ground:
d1 = (1/2) * g * t^2
Similarly, the distance covered by the second rock (d2), which took t + 1.6 seconds to hit the ground, is:
d2 = (1/2) * g * (t + 1.6)^2
We know that the distance between the rocks is 36 meters. So, we can set up the following equation:
d1 - d2 = 36
Substituting the expressions for d1 and d2, we have:
(1/2) * g * t^2 - (1/2) * g * (t + 1.6)^2 = 36
Now, we can solve this equation to find the value of "t" and ultimately the distance below the cliff at which the second stone is located.
Since the given solution is 10.97 meters, we can input this value into the equation to verify if it satisfies the equation.