Question

A flare is launched from a boat. The height, in meters, of the flare above the water is approximately by the function f(t) = -20t^2 + 120t, where t is the time in seconds after the flare is launched. How long does it take for the flare to reach its maximum height? What is the maximum height of the flare? Question 11 options: (180, 3) (68, 160) (3, 180) (6, 130)

Answer 1

The flare takes 3 seconds to reach its maximum height of 180 meters.

Step-by-step explanation:

To find the time it takes for the flare to reach its maximum height, we need to find the time at which the velocity of the flare is 0. The maximum height is reached when the velocity is 0 because the flare starts to fall back down. The velocity of the flare can be found by taking the derivative of the height function with respect to time:

v(t) = f'(t) = -40t + 120

Setting the velocity equal to 0 and solving for t:

-40t + 120 = 0

t = 3 seconds

So, it takes 3 seconds for the flare to reach its maximum height.

To find the maximum height, we substitute t = 3 into the height function:

f(3) = -20(3)^2 + 120(3) = 180 meters

Therefore, the flare reaches a maximum height of 180 meters.