Answer:
1.22 s
Step-by-step explanation:
h = -810t² + 1980t
This is the equation of a parabola.
We must solve the equation to find the maximum height (h).
The coefficient of x² is negative, so the parabola opens downward, and the vertex is a maximum.
One way to solve this problem is to convert the equation to the vertex form.
We do that by completing the square.
Calculation:
h = -810t² + 1980t
Divide both sides by -810 to make the coefficient of t² equal to 1.
(-1/810)h = t² - (22/9)t
Square half the coefficient of t
(-11/9)² = 121/81
Add and subtract it on the right-hand side
(-1/810)h = t² - (22/9)t + 121/81 - 121/81
Write the first three terms as the square of a binomial
(-1/810)h = (t - ¹¹/₉)² -121/81
Multiply both sides by -810
h = -810(t - ¹¹/₉)² + 1210
You have converted your equation to the vertex form of a parabola:
y = a(t - h)² + k = 0,
where (h, k) is the vertex.
h = ¹¹/₉ and k = 1210, so the vertex is at (¹¹/₉, 2100).
The maximum height of the rocket is 2100 cm.
After ¹¹/₉ s ≈ 1.22 s, the rocket will have reached a height of 1210 cm.
The graph below shows the rocket reaching 1210 cm at 1.22 s.
