A construction worker dropped a hammer while working on a skyscraper, 2643 feet above the ground. Use the formula [tex]$t=\frac{\sqrt{h}}{4}$[/tex] to find how many seconds it took for the hammer to reach the ground. Round to the nearest tenth of a second.
Answer (2)
Substitute the given height h = 2643 feet into the formula t = 4 h .
Calculate the square root of 2643: 2643 ≈ 51.41 .
Divide the result by 4: t = 4 51.41 ≈ 12.85 .
Round the value of t to the nearest tenth of a second: t ≈ 12.9 sec.
Explanation
Understanding the Problem We are given the height from which the hammer is dropped, which is 2643 feet. We are also given the formula to calculate the time it takes for the hammer to reach the ground: t = 4 h , where t is the time in seconds and h is the height in feet.
Substituting the Value We need to substitute the given height, h = 2643 feet, into the formula t = 4 h . So, we have: t = 4 2643
Calculating the Square Root Now, we calculate the square root of 2643: 2643 ≈ 51.41
Dividing by 4 Next, we divide the result by 4: t = 4 51.41 ≈ 12.85
Rounding to the Nearest Tenth Finally, we round the value of t to the nearest tenth of a second: t ≈ 12.9
Final Answer Therefore, it takes approximately 12.9 seconds for the hammer to reach the ground.
Examples
Imagine you are designing safety nets for construction sites. Knowing how long it takes for objects to fall from certain heights helps you determine the appropriate size and strength of the nets needed to protect workers and pedestrians. This calculation is crucial for ensuring safety on construction projects and preventing accidents.
Using the formula t = 4 h and substituting h = 2643 , we find that the time taken for the hammer to fall is approximately 12.9 seconds. After calculating the square root and dividing by 4, this value is rounded to the nearest tenth of a second. The final time it takes for the hammer to hit the ground is 12.9 seconds.
;
