Answered: If the basketball hoop is 10 feet high…

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If the basketball hoop is 10 feet high and located 15 feet away, what initial velocity v should the basketball have?

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.2: Introduction To Conics: parabolas

Problem 72E

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

How would I find the velocity of this? I’m just stuck on part a

Modeling a Foul Shot
) Shooting a Foul Shot Overhand When a basketball player shoots a foul shot, the ball follows a parabolic arc.
This arc depends on both the angle and velocity with which the basketball is released. If a person shoots the
basketball overhand from a position 8 feet above the floor, then the path can sometimes be modeled by the
-16x?
parabola
y =
0.43 v2
+1.15x + 8
50
10 ft
15 ft
where v is the velocity of the ball in feet per second, and the locations of the ball are given by the points (x, y).
a)
If the basketball hoop is 10 feet high and located 15 feet away, what initial velocity v should the basketball
have?
b) Using your v from part (a), graph the parabola using Desmos. Plot the point (0,8) where the ball is released
and the point (15, 10) where the basketball hoop is. Does your graph pass through both points?
c) What is the maximum height of the basketball? (Show ALL work)
2) Shooting a Foul Shot Underhand If a person releases a basketball underhand from a position 3 feet above the
floor, it often has a steeper arc than if it is released overhand, and the path sometimes may be modeled by
-16x2
+2.75x + 3
0.117 v2

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