Question

A ball is thrown from an initial height of 2 feet with an initial upward velocity of 21 ft/s. The ball's height h (in feet) after t seconds is given by the following.

h=2 +21t - 166
Find all values of t for which the ball's height is 8 feet.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
1 = seconds
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initial
height
ground

Answer 1

t = 0.42 or 0.89

Explanation:

We can solve the equation for h=8.

8 = 2 +21t -16t^2

6 = 21t -16t^2

-3/8 = -21/16t +t^2

-3/8 +(21/32)^2 = (21/32)^2 -21/16t +t^2 . . . . . complete the square*

57/1024 = (t -21/32)^2

t = (21 ± √57)/32 ≈ 0.4203 or 0.8922

The values of t at a height of 8 feet are 0.42 or 0.89.

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* The square is completed by adding the square of half the t-coefficient to both sides of the equation. Then we can write the variable terms as a square, take the square root, and add the opposite of the binomial constant.