A construction worker dropped a hammer while working on a skyscraper, 1752 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 height h = 1752 feet into the formula t = 4 h .
Calculate the square root of 1752: 1752 ≈ 41.8569 .
Divide the result by 4: t = 4 41.8569 ≈ 10.4642 .
Round the value of t to the nearest tenth: t ≈ 10.5 sec.
Explanation
Understanding the Problem We are given the height from which the hammer is dropped, which is 1752 feet. We are also given the formula to calculate the time it takes for the hammer to reach the ground: t = 4 h , where h is the height in feet and t is the time in seconds. Our goal is to find the time t when h = 1752 feet and round the answer to the nearest tenth of a second.
Substituting the Value of Height First, we substitute the given height h = 1752 feet into the formula: t = 4 1752
Calculating the Time Next, we calculate the square root of 1752 and divide it by 4: t = 4 1752 ≈ 4 41.8569 ≈ 10.4642
Rounding to the Nearest Tenth Finally, we round the value of t to the nearest tenth of a second: t ≈ 10.5 Therefore, it takes approximately 10.5 seconds for the hammer to reach the ground.
Examples
Understanding how long it takes for objects to fall is crucial in construction and engineering. For example, knowing the impact time of falling debris helps in designing safety nets and protective barriers around construction sites. By using the formula t = 4 h , engineers can quickly estimate the fall time from a given height, allowing them to implement appropriate safety measures to protect workers and the public. This simple calculation can significantly reduce the risk of accidents and injuries.
Using the formula t = 4 h , we find that dropping a hammer from 1752 feet takes about 10.5 seconds to reach the ground. This involves calculating the square root of 1752 and then dividing by 4. After rounding, the final answer is approximately 10.5 seconds.
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