Question

For the vertical motion model h(t) = -16t2 + 54t + 3, identify the maximum height reached by an object and the amount of time the object is in the air before it hits the ground. Round to the nearest tenth.​

Answer 1

• height: 48.6 ft
• time in air: 3.4 s

Explanation:

A graphing calculator provides a nice answer for these questions. It shows the maximum height is 48.6 feet, and the time in air is 3.4 seconds.

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The equation can be rewritten to vertex form to find the maximum height.

h(t) = -16(t^2 -54/16t) +3 . . . . . group t-terms

h(t) = -16(t^2 -54/16t +(27/16)^2) + 3 + 27^2/16

h(t) = -16(t -27/16)^2 +48 9/16

The maximum height is 48 9/16 feet, about 48.6 feet.

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The air time is found at the value of t that makes h(t) = 0.

0 = -16(t -27/16)^2 +48 9/16

(-48 9/16)/(-16) = (t -27/16)^2 . . . . . . . subtract 48 9/16 and divide by -16

(√777 +27)/16 = t ≈ 3.4297 . . . . . square root and add 27/16

The time in air is about 3.4 seconds.