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An object is dropped at rest from the top of a building of unknown height. If the object takes 3.7 seconds to land, how tall is the building in meters? Enter the value using up to two decimal places without the units.



Answer :

MathPhys

Answer:

67.08 m

Explanation:

The object is in free-fall, so it undergoes constant acceleration. The motion can be modeled using kinematic equations, also known as SUVAT equations. The equation we will use is:

s = ut + ½ at²

where

  • s is the displacement
  • u is the initial velocity
  • a is the acceleration
  • t is the time

The initial velocity is u = 0 m/s. Taking down to be positive, the acceleration is a = 9.8 m/s². The time is t = 3.7 s. Solving for the displacement:

s = ut + ½ at²

s = (0 m/s) (3.7 s) + ½ (9.8 m/s²) (3.7 s)²

s = 67.08 m

The height of the building is 67.08 meters.

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