Question

question 9 (1 point)
an emergency flare is shot vertically into the air with a speed of 60 m/s. its height h metres after t seconds is given by the equation $h = -5(t - 6)^2 + 180$.
use the above information. to the nearest second, when does the flare reach its maximum height?

after 180 seconds
after 6 seconds
after 5 seconds
after 36 seconds

Explanation:

Step1: Identify the vertex form of a parabola

The equation of the height is given in vertex form \( h = a(t - h)^2 + k \), where \((h, k)\) is the vertex. Here, the equation is \( h = -5(t - 6)^2 + 180 \), so comparing with the vertex form, we can see that \( t = 6 \) and \( h = 180 \) at the vertex.

Step2: Determine the maximum height time

Since the coefficient of \((t - 6)^2\) is negative (\(-5\)), the parabola opens downwards, so the vertex represents the maximum point. The \( t \)-coordinate of the vertex is \( 6 \), which means the flare reaches its maximum height at \( t = 6 \) seconds.

Answer:

B. After 6 seconds (assuming the option is labeled as such, with the correct option being "After 6 seconds" corresponding to the appropriate identifier, e.g., if the second option is "After 6 seconds", then the answer is the option with "After 6 seconds")