Question

a diver is standing on a platform above the pool. he jumps from the platform with an initial upward velocity of 8 ft/s. the following function represents the diver’s height (in feet) where t is time in seconds: h(t) = -16 t² + 8t + 24. how high is the platform?

Explanation:

Step1: Understand the height function

The height function is given by \( h(t) = -16t^2 + 8t + 24 \), where \( t \) is time in seconds. The platform's height is the initial height, which occurs at \( t = 0 \) (before the diver jumps, so time is 0).

Step2: Substitute \( t = 0 \) into the function

To find the initial height (platform height), we substitute \( t = 0 \) into \( h(t) \):

$$ h(0) = -16(0)^2 + 8(0) + 24 $$

Step3: Calculate the value

Simplify the expression:

$$ h(0) = 0 + 0 + 24 = 24 $$

Answer:

The platform is 24 feet high.