Vertical Displacement question

[CaYn]

Homework Statement

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 , 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 o<t<t_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.

Homework Equations

This is what I'm struggling with, I would use H(t) = v₀t + 1/2at^2, but it says to answer in terms of their vertical leap, g, and t.

The Attempt at a Solution

I don't know where to begin if I have to use the given quantities.

 

[bjd40@hotmail.com]

in yr eqn. a (acln.) should be replaced by (-g). t for ha eqn. is t and t for hb eqn. in t + tr. now subtract hb from ha. but this expression is true for t > tr. for 0<t<tr (that is the time interval when boris has not started his flight), D(t) = ha (as hb is zero for 0<t<tr). if this a textbook problem have they given the answer?

 

[CaYn]

It's a masteringphysics online, so no, they haven't given the answer.

I hate MP already xD

 

[CaYn]

I figured it out, it was just MasteringPhysics being useless

 

[rwisz]

Can you please provide more information about the problem? What is the initial velocity of the players? Are they jumping from the ground or from a certain height? Also, is there any other information given about their movements or trajectory? Without this information, it is difficult to provide a specific solution.

However, in general, the vertical displacement can be calculated using the equation D(t) = H + v0t - 1/2gt^2, where H is the initial vertical position (in this case, the height of the players' centers of mass) and v0 is the initial vertical velocity. The acceleration due to gravity, g, is a constant and can be assumed to be -9.8 m/s^2 for this problem (assuming we are using the metric system).

In terms of H, g, and t, the vertical displacement can be expressed as D(t) = H + 1/2gt^2 - 1/2gtR^2, where tR is the reaction time of Boris. This equation takes into account the fact that Arabella has already jumped and reached a certain height before Boris jumps.

Again, without more information about the problem, it is difficult to provide a more specific solution. I recommend reviewing the given information and equations, and trying different approaches to see which one makes the most sense for this problem.