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A toy rocket is launched with an initial velocity of 80 ft/s from a height of 5 ft. Write a model to express the vertical position [tex]s(t)[/tex].

Answer :

The vertical position of a toy rocket launched with an initial velocity of 80 ft/s from a height of 5 ft is modeled by the equation s(t) = 5 + 80t - 16.1t², using the physics concept of projectile motion.

To model the vertical position (s(t)) of a toy rocket shot upward with an initial velocity of 80 ft/s from a height of 5 ft, we can use the equation of motion under the influence of gravity. This question pertains to Projectile Motion in physics. The standard form of the equation that we use is:

s(t) = s₀ + v₀t + rac{1}{2}at²

Where:

  • s(t) is the vertical position as a function of time (t)
  • s₀ is the initial height (5 ft)
  • v₀ is the initial velocity (80 ft/s)
  • a is the acceleration due to gravity (-32.2 ft/s², note it's negative because gravity is acting downward)

Plugging in these values, we get:

s(t) = 5 + 80t - 16.1t²

This equation can now be used to determine the rocket's position at any time t, as long as the rocket is in projectile motion, i.e., before any other forces act on it like a parachute deployment.

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