Question

formulas involving square roots
many 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
resistance. if we want to know how long it would take for something to fall 100 fe
could substitute 100 for d.
t = 0.25√100 = 0.25(10) = 2.5 2.5 seconds
use this formula to answer each question. approximate to the nearest tenth.
how long does it take a wrench, dropped
from a 30 - foot roof, to reach the ground?
if there were no air resistance, how
long would it take an object to fall one
mile (5280 feet)?
the washington monument is 555 feet tall.
in how many seconds would an object
dropped from the top reach the ground?
if you hold out your hand and drop a
penny, about how long does it take to hit
the floor?
the formula s = 5.45√d can be used to find the speed at which an object dropped from a
height of d feet will hit the ground. the speed (s) is in miles per hour.
how fast will an object dropped from the
with no air resistance, with what speed
top of the washington monument be
would an object dropped from one mile up
going when it reaches the ground?
hit the ground?

Explanation:

1. 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

1. 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

1. 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

1. 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

1. 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

1. 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

Answer:

1. 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

1. 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

1. 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

1. 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

1. 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

1. 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