Question

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3) A diver springs up off of a diving board at an initial velocity of 24 ft/sec. The diving board is 30 feet above the water. The function that models the diver's height is: h(t) = -16t^2 + 24t + 30.

a) Find how long it takes for the diver to reach maximum height. Why can't we double this time to find how long the diver is in the air before hitting the water?

b) Determine the maximum height of the diver.

c) How far is the diver from the water after 2 seconds?

Answer 1

• a) 3/4 sec
• b) 39 feet
• c) 14 feet

Explanation:

Given function:

• h(t) = -16t^2 + 24t + 30

a) Maximum height is the vertex of the graph. Time needed:

• t = -24/2(-16) = 24/32 = 3/4 sec

If we double this time then diver will pass the peak point and it doesn't double the height

b) Maximum height is at vertex:

• h(3/4) = -16*(3/4)^2 + 24*3/4 + 30 = 39 feet

c) Distance from water after 2 seconds:

• h(2) = -16*2^2 + 24*2 + 30 = 14 feet