Projectile motion + force transfer

[eh...What]

Hello all,

I do not understand why my physics teacher does it but I just hate it when he mixes concepts from like 3 months ago with what we're on right now... this question that I am unsure of has to do with (I believe) forces and maybe-possibly projectile motion

I think It's just all gravitational potential, thou

The question asks - A basket ball player makes a free throw shot at the basket and the ball leaves the shooter's head of x (m/s) from a height of i (m) above the floor, determine the speed of the ball as it goes through the hoop at j (m) above the floor...

can I please get some clarification here? I first though of things like force transfer between the ball and the backboard and the projectile trajectory of the ball (but then I realized - no angles)...

Now I am thinking - This has only to do with Eg = mgh

am I correct? Help would be greatly appreciated! thanks!

 

[zorro]

I first though of things like force transfer between the ball and the backboard and the projectile trajectory of the ball (but then I realized - no angles)...

I assume it is a clean shot. There is no rebounding.

Now I am thinking - This has only to do with Eg = mgh

Eg?? I don't get it.
This problem can be solved by using Conservation of Energy.
The kinetic energy imparted to the ball gets converted into potential energy ( + lesser kinetic energy offcourse )

 

[collinsmark]

Hello eh...What,

Welcome to Physics Forums!

I do not understand why my physics teacher does it but I just hate it when he mixes concepts from like 3 months ago with what we're on right now...

I don't mean to be too frank, but I advise getting use to it -- not only for coursework, but also for life in general. But since we're discussing academics, I'll stick to that. If you continue studying physical sciences, the concept involved in this problem statement will come up again (many times) perhaps 3 months from now in a future course, and continuing past 6 years from now perhaps in a job interview, and many, many times later as your career continues. In physics, engineering and technology, everything you'll learn later is founded on what you're learning now.

this question that I am unsure of has to do with (I believe) forces and maybe-possibly projectile motion

I think It's just all gravitational potential, thou

[...]

can I please get some clarification here? I first though of things like force transfer between the ball and the backboard and the projectile trajectory of the ball (but then I realized - no angles)...

You could, if you really wanted to, figure out the answer to this problem using kinematics. It would take a lot of effort though. I'm guessing the solution would take at least a good page or two of paper, involve all sorts of trigonometry, simultaneous equations, geometry, and lots of simplification effort.

You are correct that no angles were given in the problem statement. But you could make some up an angle, or better yet, just keep your angles expressed in terms of variables such as θ and/or φ. It turns out that the angles will all cancel out in the end, but only after a lot of effort.

But there is an easier way (in this case).

Now I am thinking - This has only to do with Eg = mgh

Very nice! Your line of thinking is right on the mark.

am I correct?

Essentially yes. The easy solution to this problem is conservation of energy. Energy cannot be created or destroyed, it can only change form.

(In this problem we're concerned with gravitational potential energy and linear kinetic energy. Ignore thermal energy, frictional energy, rotational energy, chemical energy, atomic energy, etc., for this problem -- you'd make the same assumptions if you did the problem via kinematics anyway.)

• What is the ball's gravitational potential energy when it leaves the player's hands?
• What is the ball's linear kinetic energy when it leaves the player's hands?

• What is the ball's gravitational potential energy when it goes through the hoop?
• Knowing that energy cannot be created or destroyed, what is the ball's kinetic energy as it goes through the hoop?

The final answer should be pretty easy after that. (solve for the final velocity v_f)

(Conservation of energy makes things much, much easier if it applies. On some future problems it might not apply and you'll have to resort back to kinematics. But for the future and present problems where it does apply, you'll love how much simpler it makes things. )

[Edit: I see Abdul Quadeer beat me to the response. But even if there is a rebound off the backboard, it doesn't change the final answer, as long as frictional, rotational, energy etc., are ignored. It could bounce off the walls and ceiling and backboard, and it wouldn't change the final answer. ]

 

[eh...What]

Thanks guys !

I solved it - it's the conservation of energy where mgh1 + 1/2 mv₁² must equal mgh1 + 1/2 mv₂² ...

I feel so stupid - I never knew I can drop the m and use the equation without it...