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)
To find the distance below the cliff at which the second rock hits, we need to use the equations of motion. Let's break down the problem step by step:
Step 1: Determine the time difference (Δt) between the two rocks hitting the ground.
Given that the second rock hits 1.6 seconds after the first rock, we can denote this time difference as Δt = 1.6 s.
Step 2: Find the initial velocity of the rocks (vi).
The rocks are dropped, so their initial velocity is zero (vi = 0).
Step 3: Apply the equation of motion to find the distance traveled by each rock.
The equation for the distance traveled by an object in free fall is given by the formula:
d = vi * t + (1/2) * g * t^2
Where:
d is the distance traveled,
vi is the initial velocity,
t is the time,
and g is the acceleration due to gravity (approximately 9.8 m/s^2).
For the first rock, as it is dropped, the equation becomes:
d1 = (1/2) * g * t^2
For the second rock:
d2 = (1/2) * g * (t + Δt)^2
Step 4: Calculate the value of g, the acceleration due to gravity.
The acceleration due to gravity on Earth is approximately 9.8 m/s^2.
Step 5: Use the equations to find the distances traveled by the rocks.
Substitute the values into the equations:
d1 = (1/2) * 9.8 * (1.6^2)
d2 = (1/2) * 9.8 * (1.6 + 1.6)^2
Simplify and calculate:
d1 = 9.8 * 1.6^2 = 9.8 * 2.56 = 25.088 m
d2 = 9.8 * (3.2)^2 = 9.8 * 10.24 = 100.352 m
Step 6: Find the distance between the two rocks.
The distance between the two rocks is 36 m.
Step 7: Determine the distance below the cliff at which the second rock hits.
We subtract the distance traveled by the first rock from the total distance to find the distance at which the second rock hits:
d2 - d1 = 100.352 m - 25.088 m = 75.264 m
Therefore, the second rock hits at a distance of 75.264 meters below the cliff.
Please note that the value provided (10.97 m) does not match the calculated value, so it seems there might be an error in the problem or calculation.