Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Basketball

If a basketball player shoots  an underhand foul shot, releasing the ball at a 70° angle from a position 3.5 feet above the floor, then the path of the ball can be modeled by the function

h(x) = -(136x^2)/(v^2) + 2.7x + 3.5,

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.

A. The center of the hoop is 10 feet above the floor and 15 feet in front of the foul line. Determine the initial velocity with which the ball must be shot in order for the ball to go through the hoop.

B. Write a function for the path of the ball using the velocity found in part A above.

C. Determine the height of the 84 after it has traveled 9 feet in front of the basketball.

Part A

I must let h(x) = 10 and x = 15 and solve for v. You say?

Part B

I need help for part B.

Part C

Let x = 9 and v = the velocity found in part A.

You say?

Part D

To find additional points, I must create a table in terms if x and h(x).

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Basketball

A correct.

That will give a V value.  I haven't tried it. Let's say V = 20

Then the function becomes -136x^2/400 + 2.7x + 3.5

So you can proceed with that for the rest of the questions.

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

A correct.

That will give a V value.  I haven't tried it. Let's say V = 20

Then the function becomes -136x^2/400 + 2.7x + 3.5

So you can proceed with that for the rest of the questions.

Bob

Thank you. Looks good. I will proceed and show my work when time allows.

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Basketball

...the path of the ball can be modeled by the function h(x) = -(136x^2)/(v^2) + 2.7x + 3.5, 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.

Part B. Write a function for the path of the ball using the velocity found in part A above.

I need help for part B.

Once you get the number for 'v' from part 'A', plug that into the eqn they gave you
(and maybe simplify)
That's all they want for this part

Part D. To find additional points, I must create a table in terms if x and h(x).

What were the instructions for this part?
(it's not in your first post, i don't think?)

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Basketball

...the path of the ball can be modeled by the function h(x) = -(136x^2)/(v^2) + 2.7x + 3.5, 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.

Part B. Write a function for the path of the ball using the velocity found in part A above.

I need help for part B.

Once you get the number for 'v' from part 'A', plug that into the eqn they gave you
(and maybe simplify)
That's all they want for this part

Part D. To find additional points, I must create a table in terms if x and h(x).

What were the instructions for this part?
(it's not in your first post, i don't think?)

Instructions are clearly given in this question.

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Basketball

A. The center of the hoop is 10 feet above the floor and 15 feet in front of the foul line. Determine the initial velocity with which the ball must be shot in order for the ball to go through the hoop.

B. Write a function for the path of the ball using the velocity found in part A above.

C. Determine the height of the 84 after it has traveled 9 feet in front of the basketball.

The only instrutions Im' seeing are the 3 quoted
sorry

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Basketball

A. The center of the hoop is 10 feet above the floor and 15 feet in front of the foul line. Determine the initial velocity with which the ball must be shot in order for the ball to go through the hoop.

B. Write a function for the path of the ball using the velocity found in part A above.

C. Determine the height of the 84 after it has traveled 9 feet in front of the basketball.

The only instrutions Im' seeing are the 3 quoted
sorry

Can you help me with Part B?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Basketball

What did you get for part A ?

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

What did you get for part A ?

Bob

I didn't do part A so far. I will try it later. Very busy this morning.

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Basketball

Can you help me with Part B?

find 'v' for part A
plug that into the eqn they gave you
this is all they want for partt B

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Basketball

Can you help me with Part B?

find 'v' for part A
plug that into the eqn they gave you
this is all they want for partt B

Copy. Understood. More math later tonight.