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The formula S=16t^(2) is used to approximate the distance S, in feet, that an object falls freely from rest in t seconds. The height of a building is 1390 feet. How long would it take for an object to fall from the top?

The formula S=16t2 S=16 t^{2} is used to approximate the distance S S , in feet, that an object falls freely from rest in t t seconds. The height of a building is 13901390 feet. How long would it take for an object to fall from the top?

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Q. The formula S=16t2 S=16 t^{2} is used to approximate the distance S S , in feet, that an object falls freely from rest in t t seconds. The height of a building is 13901390 feet. How long would it take for an object to fall from the top?
  1. Identify Formula and Height: Identify the given formula and the height of the building.\newlineThe formula given is S=16t2S = 16t^2, which is used to approximate the distance SS, in feet, that an object falls freely from rest in tt seconds. The height of the building is given as 13901390 feet.
  2. Set Equation for t: Set the formula equal to the height of the building to solve for t. We have S=1390S = 1390 feet, so we set the equation 16t2=139016t^2 = 1390.
  3. Isolate t2t^2: Divide both sides of the equation by 1616 to isolate t2t^2.\newlinet2=139016t^2 = \frac{1390}{16}\newlinet2=86.875t^2 = 86.875
  4. Solve for tt: Take the square root of both sides to solve for tt.t=86.875t = \sqrt{86.875}t≈9.32t \approx 9.32 seconds

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