Thank you for visiting A basketball is thrown with an initial upward velocity of 23 feet per second from a height of 7 feet above the ground The equation. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Final answer:
Given the provided motion physics model and using the quadratic formula, it is determined that it would take approximately 3.79 seconds for the basketball to go into the hoop after it was thrown.
Explanation:
The subject in consideration here is a problem related to quadratic equations in motion physics. The equation given in the question signifies a model of the height of the basketball as a function of time in the format of a quadratic equation. The equation is h = -16t² + 23t + 7.
With this equation, we can apply the quadratic formula to find the amount of time it takes for the ball to reach the hoop.
Upon using the quadratic formula, two solutions come up, t = 3.79 s and t = 0.54 s. The ball is at a height of 10 m at two times during its trajectory—once on the way up (as it rises) and once on the way down (as it falls). Since the question is about the time the ball goes into the hoop after reaching its maximum height and coming down, the larger value of t (3.79s) is considered as the valid solution.
Therefore, the time it takes for the basketball to go into the hoop after it was thrown is approximately 3.79 seconds which is not an offered option.
Learn more about quadratic equations here:
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Rewritten by : Jeany
10=-16t^2+23t+7 subtracting the right side from both sides
16t^2-23t+3=0 using the quadratic formula
t=(23±√337)/32, since we are looking for the larger value of t, as the ball in returning downward...
t=(23+√337)/32
t≈1.29 seconds
16t^2-23t+3=0 using the quadratic formula
t=(23±√337)/32, since we are looking for the larger value of t, as the ball in returning downward...
t=(23+√337)/32
t≈1.29 seconds
