Question

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a basketball players hang time is the time spent in the air when shooting a basket. the formula $t = \frac{\sqrt{d}}{2}$ models hang time, t, in seconds, in terms of the vertical distance of a players jump, d, in feet. when a particular player dunked a basketball, his hang time for the shot was approximately 1.14 seconds. what was the vertical distance, d, of his jump, rounded to the nearest tenth?
the jump was \\(\square\\) feet. (round to the nearest tenth as needed.)

Explanation:

Step1: Substitute given t into formula

$1.14 = \frac{\sqrt{d}}{2}$

Step2: Isolate the square root term

Multiply both sides by 2:
$1.14 \times 2 = \sqrt{d}$
$2.28 = \sqrt{d}$

Step3: Solve for d by squaring both sides

$d = 2.28^2$
$d = 5.1984$

Step4: Round to nearest tenth

$d \approx 5.2$

Answer:

5.2