QuestionMay 13, 2025

A window washer drops a bucket from the top of a 256 foot building. The height h of the bucket after t seconds is given by h=-16t^2+256 When will the bucket hit the ground?

A window washer drops a bucket from the top of a 256 foot building. The height h of the bucket after t seconds is given by h=-16t^2+256 When will the bucket hit the ground?
A window washer drops a bucket from the top of a 256 foot building. The height h of the bucket after t seconds is given by h=-16t^2+256 When will the bucket hit the ground?

Solution
4.1(235 votes)

Answer

4 seconds Explanation 1. Set the height equation to zero The bucket hits the ground when h = 0. Set -16t^2 + 256 = 0. 2. Solve for t Rearrange to 16t^2 = 256. Divide both sides by 16 to get t^2 = 16. 3. Calculate the square root Take the square root of both sides: t = \sqrt{16} = 4.

Explanation

1. Set the height equation to zero<br /> The bucket hits the ground when $h = 0$. Set $-16t^2 + 256 = 0$.<br />2. Solve for t<br /> Rearrange to $16t^2 = 256$. Divide both sides by 16 to get $t^2 = 16$.<br />3. Calculate the square root<br /> Take the square root of both sides: $t = \sqrt{16} = 4$.
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