Question

A body is dropped from the roof of a 20 m high building by how much:

Does it take to reach the ground? How fast does it hit the ground?

Answer 1

t = 2.01 s

Vf = 19.7 m/s

Step-by-step explanation:

It's know through the International System that the earth's gravity is 9.8 m/s², then we have;

Data:

• Height (h) = 20 m
• Gravity (g) = 9.8 m/s²
• Time (t) = ?
• Final Velocity (Vf) = ?

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Time

Use formula:

• 
  `\boxed{t=\sqrt{(2*h)/(g)}}`

Replace:

• 
  `\boxed{t=\sqrt{(2*20m)/(9.8(m)/(s^(2)))}}`

Everything inside the root is solved first. So, we solve the multiplication of the numerator:

• 
  `\boxed{t=\sqrt{(40m)/(9.8(m)/(s^(2)))}}`

It divides:

• 
  `\boxed{t=√(4.08s)}`

The square root is performed:

• 
  `\boxed{t=2.01s}`

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Final Velocity

use formula:

• Vf = g * t

Replace:

• Vf = 9.8 m/s² * 2.01 s

Multiply:

• Vf = 19.7 m/s

==================================================================

How long does it take to reach the ground?

Takes time to reach the ground in 2.01 seconds.

How fast does it hit the ground?

Hits the ground with a speed of 19.7 meters per seconds.