Jivesh is analyzing the flight of a few of his model rockets with various equations. In each equation, h is
the height of the rocket in centimeters, and the rocket was fired from the ground at time t = 0, where t is
measured in seconds.
Jivesh also has a more powerful Model B rocket. For this rocket, he uses the equation h =-81012+1,980t.
When is the height of the Model B rocket 1,210 centimeters? Round your answers to the nearest
hundredth.
After how t “” seconds, the rocket will have reached a height of 1,210 centimeters

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.