Vertical displacement basketball problem

[dude24]

Two basketball players are essentially equal in all respects. (They are the same height, they jump with the same initial velocity, etc.) In particular, by jumping they can raise their centers of mass the same vertical distance, H (called their "vertical leap").

The first player, Arabella, wishes to shoot over the second player, Boris, and for this she needs to be as high above Boris as possible. Arabella jumps at time t=0, and Boris jumps later, at time t_R (his reaction time).

Assume that Arabella has not yet reached her maximum height when Boris jumps.


Find the vertical displacement D(t) = h_A(t) - h_B(t), as a function of time for the interval 0 < t < t_{\rm R}, where h_A(t) is the height of the raised hands of Arabella, while h_B(t) is the height of the raised hands of Boris.

Express the vertical displacement in terms of H, g, and t.
I need help figuring out this equation!


Find the vertical displacement D(t) between the raised hands of the two players for the time period after Boris has jumped (t>t_{\rm R}) but before Arabella has landed.

Express your answer in terms of t, t_R, g, and H.
I need help figuring out this equation!

 

[Astronuc]

See - http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html
Click on vertical launches.

Now before t_R, Boris is stationary, so h_B(t) = 0, assuming both A and B's hands start at the same height.

Now one has to find the h_A(t). What is her initial velocity?

Well, we can obtain this from knowing her max jump height H.

Use conservation of energy - initial KE = 1/2 mv² = Grav. Pot. Energy = mgH. The mass cancels, and . . . . .

Now apply the appropriate equation for h_A(t) with the initial velocity as function of H and constant deceleration of g.

Now after t_R, Boris jumps with the same trajectory (equation), but t-t_R rather than t, since his trajectory is delayed by t_R.

 

[fubag]

one more question surrounding this problem:

What advice would you give Arabella to minimize the chance of her shot being blocked?
A. Shoot when you have the maximum vertical velocity.

B. Shoot at the instant Boris leaves the ground.

C. Shoot when you have the same vertical velocity as Boris.

D. Shoot when you reach the top of your jump (when your height is H).

By common sense I can omit D, and B as it doesn't make much sense.

Any help will be deeply appreciated.

 

[learningphysics]

i need a bit more help in the second part of the problem...


I do not quite understand how we can now solve for Boris' time.

Thanks

What did you get for the first part?

 

[fubag]

Sorry i got the first and second parts...

looks like the forum takes time to update.

 

[learningphysics]

Sorry i got the first and second parts...

looks like the forum takes time to update.

why doesn't B make sense to you?

 

[fubag]

ok, so I am assuming that if arabella jumps before boris she is guranteed almost no blocking, as compared to all the rest of the choices?

can you explain why A and C are not valid choices?

 

[learningphysics]

ok, so I am assuming that if arabella jumps before boris she is guranteed almost no blocking, as compared to all the rest of the choices?

can you explain why A and C are not valid choices?

I think the only factor is the height difference... I don't think it matters what velocities of boris and arabella are... I think the height difference is all the affects the choice... maximum height difference => less chance of blocking...

 

[kaykay6]

So you are supposed to view the first part of the problem, solving for displacement in terms of H (vertical distance), g, and t in terms of conservation of energy? I'm confused on how to derive that vertical displacement equation.