The formula h=280t-7t^2 gives the height, h in meters, of a rocket t seconds after take off. The maximum height reached by the rocket is 2800 m. How long will it take the rocket to reach this maximum height?

h = 280t - 7t^2 = 2800.

-7t^2 + 280t - 2800 = 0
Use Quadratic Formula.
t = 20 s.

To find the time it takes for the rocket to reach its maximum height, we need to determine the value of t when the height, h, is at its maximum. In this case, the maximum height is given as 2800 meters.

The formula for the height of the rocket is given as h = 280t - 7t^2, where h is the height in meters and t is the time in seconds.

To find the time it takes for the rocket to reach maximum height, we can set up an equation:

280t - 7t^2 = 2800

Now, let's rearrange the equation to put it in quadratic form:

7t^2 - 280t + 2800 = 0

Next, we can solve this quadratic equation to find the values of t. We can either factor the equation or use the quadratic formula. Let's use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Where a = 7, b = -280, and c = 2800.

Plugging these values into the formula:

t = (-(-280) ± √((-280)^2 - 4 * 7 * 2800)) / (2 * 7)

Simplifying further:

t = (280 ± √(78400 - 78400)) / 14

Since the discriminant (b^2 - 4ac) is zero, there will be only one value of t. Continuing with the simplification:

t = 280 / 14

t = 20

Therefore, it will take the rocket 20 seconds to reach its maximum height of 2800 meters.