To find the maximum height attained by the object described by the equation h = 10t – 5t², we can use calculus or complete the square.
This equation is a quadratic function of the form h(t) = at² + bt + c, where:
- a = -5, which is negative, indicating that the parabola opens downward and thus has a maximum point.
- b = 10, and
- c = 0.
To find the time t at which the maximum height occurs, we can use the vertex formula for a quadratic equation:
t = -b / (2a)
Substituting in our values:
- t = -10 / (2 * -5) = -10 / -10 = 1
Now, we will substitute t = 1 back into the height equation to find the maximum height:
h(1) = 10(1) – 5(1)²
- h(1) = 10 – 5 = 5
Therefore, the maximum height attained by the object is 5 meters.