Two stones are dropped from the edge of a 60-m cliff, the seconds stone 1.6s after the first. How far below the top of the cliff is the second stone when the separation between the two stones is 36 m?
need answer
The distance between them is 9m
To solve this problem, we can use the kinematic equations of motion. Let's define the following variables:
h = Height of the cliff (60 m)
t = Time when the second stone is dropped (1.6 s)
d = Separation between the two stones (36 m)
s1 = Distance traveled by the first stone (unknown)
s2 = Distance traveled by the second stone (unknown)
We'll start by finding the time it takes for the first stone to reach the ground. We'll use the equation:
h = (1/2) * g * t^2
Substituting the given values, we can solve for t:
60 = (1/2) * 9.8 * t^2
t^2 = (2 * 60) / 9.8
t^2 ≈ 12.24
t ≈ √12.24
t ≈ 3.5 s (approximately)
So it takes approximately 3.5 seconds for the first stone to reach the ground.
Next, we'll find the time it takes for the second stone to reach the ground. We'll subtract the time it takes for the first stone to reach the ground from the time when the second stone is dropped:
t2 = t - 1.6
t2 = 3.5 - 1.6
t2 ≈ 1.9 s (approximately)
Therefore, it takes approximately 1.9 seconds for the second stone to reach the ground.
Now, we can calculate the distances traveled by each stone using the equation:
s = (1/2) * g * t^2
For the first stone:
s1 = (1/2) * 9.8 * (3.5)^2
s1 ≈ 60.8 m (approximately)
For the second stone:
s2 = (1/2) * 9.8 * (1.9)^2
s2 ≈ 17.3 m (approximately)
Finally, we can find the distance below the top of the cliff for the second stone by subtracting the separation distance from the distance traveled by the second stone:
Distance below the top for the second stone = s2 - d
Distance below the top for the second stone ≈ 17.3 - 36
Distance below the top for the second stone ≈ -18.7 m (approximately)
Hence, the second stone is approximately 18.7 meters above the top of the cliff when the separation between the two stones is 36 meters.
To solve this problem, we need to find the time it takes for each stone to reach the separation distance of 36 meters below the top of the cliff.
Let's start by considering the first stone that was dropped. We know that it takes some time for the stone to fall 36 meters. We can use the formula to calculate the distance fallen by an object in free fall:
d = (1/2) * g * t^2
Where:
d is the distance fallen (36 meters in this case),
g is the acceleration due to gravity (approximately 9.8 m/s^2 near the Earth's surface),
t is the time taken (which we need to find).
Rearranging the equation, we have:
t = sqrt((2 * d) / g)
t = sqrt((2 * 36) / 9.8)
t ≈ 2.7 seconds
So, it took approximately 2.7 seconds for the first stone to fall 36 meters below the top of the cliff.
Now, let's consider the second stone. It was dropped 1.6 seconds after the first stone, so it had less time to fall. We can find the fall time for the second stone by subtracting 1.6 seconds from the fall time of the first stone:
t2 = t1 - 1.6
t2 ≈ 2.7 - 1.6
t2 ≈ 1.1 seconds
Therefore, the second stone took approximately 1.1 seconds to fall from the top of the cliff to the separation distance of 36 meters.
To find the distance below the top of the cliff where the second stone is when the separation between the two stones is 36 meters, we can now calculate the distance fallen by the second stone in 1.1 seconds using the same equation:
d2 = (1/2) * g * t2^2
d2 = (1/2) * 9.8 * (1.1)^2
d2 ≈ 6.05 meters
Therefore, the second stone is approximately 6.05 meters below the top of the cliff when the separation between the two stones is 36 meters.