Math Problem Statement

Solve

A model rocket is launched vertically upward from the ground with an initial velocity of 32 ft/s. The height of the rocket in feet after t seconds is given by s(t) = -16t^2 + 32t. When is the rocket at a height of 16 ft? Enter an exact answer.

Solution

The rocket reaches a height of 16 feet at t=1t = 1 second.

Would you like further details or explanations? Here are some related questions to expand upon this concept:

  1. How long does the rocket take to reach its maximum height?
  2. What is the maximum height the rocket will reach?
  3. When will the rocket hit the ground again?
  4. What is the rocket's velocity at t=1t = 1 second?
  5. Can you find the time interval when the rocket is above 16 feet?

Tip: The equation s(t)=16t2+32ts(t) = -16t^2 + 32t models the height of the rocket over time, where the coefficient of t2t^2 comes from gravitational acceleration.

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Math Problem Analysis

Mathematical Concepts

Quadratic Equations
Projectile Motion
Algebra

Formulas

s(t) = -16t^2 + 32t
Quadratic equation formula: ax^2 + bx + c = 0

Theorems

Quadratic Formula

Suitable Grade Level

Grades 9-12