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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?

Sagot :

Alejanndraaxidn

Answer:

t = 2.01 s

Vf = 19.7 m/s

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) = ?

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

Time

Use formula:

  • [tex]\boxed{t=\sqrt{\frac{2*h}{g}}}[/tex]

Replace:

  • [tex]\boxed{t=\sqrt{\frac{2*20m}{9.8\frac{m}{s^{2}}}}}[/tex]

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

  • [tex]\boxed{t=\sqrt{\frac{40m}{9.8\frac{m}{s^{2}}}}}[/tex]

It divides:

  • [tex]\boxed{t=\sqrt{4.08s}}[/tex]

The square root is performed:

  • [tex]\boxed{t=2.01s}[/tex]

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

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.

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