A ball is shot from a cannon into the air with an upward velocity of 3...
Understanding the Height EquationThe height of the ball is described by the quadratic equation:
h(t) = -16t² + 36t + 1.5
This equation represents a parabola that opens downwards, indicating that the ball will reach a maximum height before falling back down.
Finding the Maximum HeightTo find the maximum height, we can use the vertex formula of a quadratic equation. The time (t) at which the maximum height occurs can be found using:
t = -b / (2a)
where:
- a = -16 (coefficient of t²)
- b = 36 (coefficient of t)
Calculating Time of Maximum HeightSubstituting the values into the formula:
t = -36 / (2 * -16)
t = -36 / -32
t = 1.125 seconds
This is the time at which the maximum height is reached.
Calculating Maximum HeightNow, substitute t back into the height equation to find h(1.125):
h(1.125) = -16(1.125)² + 36(1.125) + 1.5
h(1.125) = -16(1.265625) + 40.5 + 1.5
h(1.125) = -20.25 + 40.5 + 1.5
h(1.125) = 21.75 ft
ConclusionThe maximum height attained by the ball is:
21.75 ft
Thus, the correct answer is option 'A'.