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A ball is thrown vertically upward from the top of a 100-foot tower, with an initial velocity of 20 ft/sec. Its position function is s(t) = -16t^2 + 20t + 100. What is its velocity in ft/sec when t = 1 second?

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Lanuel

The velocity of the ball in ft/sec, when t = 1 second is equal to -12 ft/sec.

Given the following data:

  • Displacement = 100 feet
  • Time = 1 seconds
  • Position function = [tex]s(t) = -16t^2 + 20t + 100[/tex]

To calculate the velocity of the ball in ft/sec, when t = 1 second:

Mathematically, the velocity of an object or physical body is equal to the differentiation of it's position function.

Velocity = s'(t)

Velocity = [tex]s(t) = -16t^2 + 20t + 100[/tex]

[tex]Velocity = -32t + 20[/tex]

Substituting the value of time (t), we have:

[tex]Velocity = -32(1) +20\\\\Velocity =-32+20[/tex]

Velocity = -12 ft/sec

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