formulas involving square roots\nmany useful formulas contain square roots. the formula t = 0.25√d gives the…

formulas involving square roots\nmany useful formulas contain square roots. the formula t = 0.25√d gives the seconds (t) it would take an object to fall d feet after being dropped if there\nresistance. if we want to know how long it would take for something to fall 100 fe\ncould substitute 100 for d.\nt = 0.25√100 = 0.25(10) = 2.5 2.5 seconds\nuse this formula to answer each question. approximate to the nearest tenth.\nhow long does it take a wrench, dropped\nfrom a 30 - foot roof, to reach the ground?\nif there were no air resistance, how\nlong would it take an object to fall one\nmile (5280 feet)?\nthe washington monument is 555 feet tall.\nin how many seconds would an object\ndropped from the top reach the ground?\nif you hold out your hand and drop a\npenny, about how long does it take to hit\nthe floor?\nthe formula s = 5.45√d can be used to find the speed at which an object dropped from a\nheight of d feet will hit the ground. the speed (s) is in miles per hour.\nhow fast will an object dropped from the\nwith no air resistance, with what speed\ntop of the washington monument be\nwould an object dropped from one mile up\ngoing when it reaches the ground?\nhit the ground?

Answer

For the wrench dropped from a 30 - foot roof:
- Answer:
  - (t\approx1.4) seconds
- Explanation:
  - Step1: Identify the formula and value of (d)
    - The formula is (t = 0.25\sqrt{d}), and (d = 30).
  - Step2: Calculate the square - root of (d)
    - (\sqrt{30}\approx5.477)
  - Step3: Multiply by 0.25
    - (t=0.25\times5.477 = 1.36925\approx1.4) seconds
For an object falling one mile (5280 feet):
- Answer:
  - (t\approx18.5) seconds
- Explanation:
  - Step1: Identify the formula and value of (d)
    - The formula is (t = 0.25\sqrt{d}), and (d = 5280).
  - Step2: Calculate the square - root of (d)
    - (\sqrt{5280}\approx72.664)
  - Step3: Multiply by 0.25
    - (t = 0.25\times72.664=18.166\approx18.5) seconds
For an object dropped from the top of the Washington Monument (555 feet):
- Answer:
  - (t\approx5.9) seconds
- Explanation:
  - Step1: Identify the formula and value of (d)
    - The formula is (t = 0.25\sqrt{d}), and (d = 555).
  - Step2: Calculate the square - root of (d)
    - (\sqrt{555}\approx23.559)
  - Step3: Multiply by 0.25
    - (t=0.25\times23.559 = 5.88975\approx5.9) seconds
For a penny dropped (assuming a typical hand - to - floor height, say 4 feet):
- Answer:
  - (t\approx0.5) seconds
- Explanation:
  - Step1: Identify the formula and value of (d)
    - The formula is (t = 0.25\sqrt{d}), and (d = 4).
  - Step2: Calculate the square - root of (d)
    - (\sqrt{4}=2)
  - Step3: Multiply by 0.25
    - (t=0.25\times2 = 0.5) seconds
For the speed of an object dropped from the top of the Washington Monument (555 feet):
- Answer:
  - (s\approx128.3) miles per hour
- Explanation:
  - Step1: Identify the formula and value of (d)
    - The formula is (s = 5.45\sqrt{d}), and (d = 555).
  - Step2: Calculate the square - root of (d)
    - (\sqrt{555}\approx23.559)
  - Step3: Multiply by 5.45
    - (s=5.45\times23.559 = 128.39655\approx128.3) miles per hour
For the speed of an object dropped from one mile up (5280 feet):
- Answer:
  - (s\approx396.0) miles per hour
- Explanation:
  - Step1: Identify the formula and value of (d)
    - The formula is (s = 5.45\sqrt{d}), and (d = 5280).
  - Step2: Calculate the square - root of (d)
    - (\sqrt{5280}\approx72.664)
  - Step3: Multiply by 5.45
    - (s=5.45\times72.664 = 396.0188\approx396.0) miles per hour