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CAN SOMEONE HELP WITH THIS QUESTION?

CAN SOMEONE HELP WITH THIS QUESTION?-example-1

1 Answer

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Answer:

  • v(t) = 38 -9.8t
  • h(t) = -4.9t² +38t +1.8

Explanation:

You want functions for the velocity v(t) and height h(t) of a ball thrown upward at 38 m/s from a height of 1.8 m. The acceleration is -9.8 m/s².

Relations

This sort of problem is usually discussed in a physics course. The relation between acceleration, velocity, and position is ...

velocity is the rate of change of position

acceleration is the rate of change of velocity

Then the inverse relations are ...

h(t) = ∫v(t)dt +h(0)

v(t) = ∫a(t)dt +v(0)

Application

When position is measured in one dimension (up = positive), these have the standard formulas:

v(t) = g·t + v(0)

h(t) = 1/2g·t² +v(0)·t +h(0)

Filling in the given values (g = -9.8, v(0) = 38, h(0) = 1.8), we have ...

v(t) = -9.8t +38 . . . . . . . . . . . . meters per second

h(t) = -4.9t² +38t +1.8 . . . . . . meters

User Josh Bernfeld
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