a stone falls from a cliff and travels 34.3m in the last second before it reaches the ground. calculate the height of the cliff.
To calculate the height of the cliff, we can use the equation of motion for free-falling objects:
s = ut + (1/2)gt^2
Where:
s = distance traveled (34.3m in this case)
u = initial velocity (0 m/s as the stone is dropped from rest)
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time taken (1 second in this case)
Substituting the values into the equation:
34.3 = 0 + (1/2)(9.8)(1^2)
34.3 = 4.9
Therefore, the height of the cliff is approximately 34.3 meters.
To calculate the height of the cliff, we can use the formula for the distance traveled by a falling object:
d = (1/2) * g * t^2
Here, "d" represents the distance, "g" is the acceleration due to gravity, and "t" is the time. In this case, we know that the stone travels 34.3 meters in the last second before it reaches the ground.
Since the time traveled in the last second is 1 second, we can substitute those values into the formula:
34.3 = (1/2) * g * 1^2
Now, we can solve this equation to find the value of the acceleration due to gravity (g). Rearranging the equation, we have:
34.3 = (1/2) * g
Multiplying both sides of the equation by 2, we get:
68.6 = g
Now that we know the acceleration due to gravity is 68.6 m/s^2, we can use this value to calculate the height of the cliff.
Using the formula for distance traveled by a falling object, we can rearrange the equation to solve for "t" (time):
d = (1/2) * g * t^2
Plugging in the values we have:
h = (1/2) * 68.6 * t^2
To find the height of the cliff, we need to find the total time (t) it takes for the stone to fall from the cliff to the ground. We know that the last second the stone travels before reaching the ground is 1 second.
So, the total time (t) will be the sum of the time it takes for the stone to travel 34.3m (in the last second) and the remaining time it takes to reach the ground from the starting point of the last second.
Now, let's calculate the remaining time it takes to reach the ground from the starting point of the last second. We know that the distance traveled by the stone during this time is the height of the cliff (h). Substituting the values in the formula:
h = (1/2) * 9.8 * t^2
Simplifying this equation:
h = 4.9 * t^2
Now, we can find the total time (t) using the equation:
34.3 = 4.9 * t^2
Rearranging the equation:
t^2 = 34.3 / 4.9
t^2 ≈ 7
Taking the square root of both sides:
t ≈ √7
So, the total time (t) it takes for the stone to fall from the cliff to the ground is approximately √7 seconds.
Now, let's calculate the height of the cliff by substituting the value of t back into the equation:
h = 4.9 * (√7)^2
h ≈ 4.9 * 7
h ≈ 34.3
Therefore, the height of the cliff is approximately 34.3 meters.
I didnt get it
Let T be the total time to fall.
Let H be the cliff height.
You must solve two equations in two unkonowns. No big deal.
H = (1/2) g T^2
H - 34.3 = (1/2) g (T-1)^2
First eliminate H
34.3 = (g/2)[T^2 - T^2 +2T -1]
= (g/2)(2T-1)
(2T-1) = 7.0 s
T = 4.0 s
Then solve for H. I get 78.4 m.