Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Basketball Foul Shots

If a basketball player shoots a foul shot, releasing the ball at a 45-degree angle from a position 6 feet above the floor, then the path of the ball can be modeled by the function h(x) = -(44x^2)/(v^2) + x + 6, where h is the height of the ball above the floor, x is the forward distance of the ball in front of the foul line, and v is the initial velocity with which the ball is shot  in feet per second. Suppose a player shoots a ball with an initial velocity of 28 feet per second. The center of the hoop is 10 feet above the floor and 15 feet in front of the foul line.

A. Will the ball go through the hoop? Why? Why not?

B. If not, with what initial velocity must the ball be shot in order for the ball to go through the hoop?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Basketball Foul Shots

You've got a value for v and for x so you can find h.  Is it a goal winning height?

Strictly  the ball has to reach a height higher, just short of the hoop and then have the ball drop down into the hoop; or clear it but bounce of the backboard to drop in; but I don't think the setter of this question wanted you to be that exact; just get the ball to 10 feet when x = 15 feet.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Basketball Foul Shots

You've got a value for v and for x so you can find h.  Is it a goal winning height?

Strictly  the ball has to reach a height higher, just short of the hoop and then have the ball drop down into the hoop; or clear it but bounce of the backboard to drop in; but I don't think the setter of this question wanted you to be that exact; just get the ball to 10 feet when x = 15 feet.

Bob

Can you set up the function for me?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Basketball Foul Shots

h(x) = -(44x^2)/(v^2) + x + 6

v = 28  x = 15

h(x) = -(44 times 15^2)/(28^2) + 15 + 6

Is this 10 ? I assume not or part b is pointless.

h(x) = -(44x^2)/(v^2) + x + 6, So calculate v when x = 15 and h = 10

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Basketball Foul Shots

h(x) = -(44x^2)/(v^2) + x + 6

v = 28  x = 15

h(x) = -(44 times 15^2)/(28^2) + 15 + 6

Is this 10 ? I assume not or part b is pointless.

h(x) = -(44x^2)/(v^2) + x + 6, So calculate v when x = 15 and h = 10

Bob

Where do I plug h in the function?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Basketball Foul Shots

LHS. Then re-arrange to get v.

B

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Basketball Foul Shots

Can you set up the function for me?

They gave you

They ask if the equation works with

So see if it works

Simplify
does this equal 10?

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Basketball Foul Shots

Can you set up the function for me?

They gave you

They ask if the equation works with

So see if it works

Simplify
does this equal 10?

The answer is not 10.