A stone is dropped from a cliff 344 feet high. after how many seconds will it be 200 feet above the ground?
height = -16t^2 + 344
when height = 200
16t^2 = 144
t^2 = 144/16
t = 3
after 3 seconds it will be 200 ft high
Well, let's try not to drop any stones here, but I can definitely help you with the math! We can use the formula for free fall distance, which is given by:
h = (1/2)gt^2
Where h is the distance, g is the acceleration due to gravity (approximately 32.2 feet/s^2), and t is the time in seconds.
Given that the stone is dropped from a 344 feet high cliff, we can set up the equation like this:
344 - 200 = (1/2)(32.2)t^2
Solving for t, we get:
144 = 16.1t^2
Dividing both sides by 16.1, we have:
t^2 = 8.94
Taking the square root of both sides, we find:
t ≈ 2.99 seconds
So, after approximately 3 seconds, the stone will be 200 feet above the ground. But I must say, the stone won't appreciate the height jokes!
To find the time it takes for the stone to be 200 feet above the ground, we can use the equations of motion for a freely falling object. The equation we will use is:
\( s = ut + \frac{1}{2}gt^2 \)
Where:
- \( s \) is the distance traveled by the object
- \( u \) is the initial velocity (in this case, 0 since the stone is dropped)
- \( g \) is the acceleration due to gravity (approximately \( 32 \, \text{ft/s}^2 \))
- \( t \) is the time taken
We can rearrange the equation to solve for time:
\( t = \sqrt{\frac{2(s-u)}{g}} \)
In this case, the initial distance from which the stone is dropped is 344 feet, and we want to know the time it takes for the stone to be 200 feet above the ground.
Using the equation, we can calculate the time:
\( t = \sqrt{\frac{2(200-0)}{32}} \)
\( t = \sqrt{\frac{400}{32}} \)
\( t = \sqrt{12.5} \)
\( t \approx 3.54 \) seconds
Therefore, it will take approximately 3.54 seconds for the stone to be 200 feet above the ground.
To find the time it takes for the stone to be 200 feet above the ground, we can use the equation of motion for free-falling objects. The equation is:
h = (1/2)gt^2
Where:
h = height (in this case, the initial height of the stone)
g = acceleration due to gravity (approximately 32.2 ft/s^2)
t = time (in seconds)
In this problem, we know the initial height of the stone is 344 feet and we want to find the time it takes for the stone to be 200 feet above the ground. Let's solve for time:
200 = (1/2)(32.2)t^2
To simplify, we will divide both sides of the equation by 16.1 (which is half of 32.2):
12.422360248447205 = t^2
Next, we take the square root of both sides to find t:
t = √(12.422360248447205)
Using a calculator, we find that t ≈ 3.52 seconds.
Therefore, it will take approximately 3.52 seconds for the stone to be 200 feet above the ground.