Physics Trick Needed

Question

I am getting this problem while adding features to my game boss . One of the attack boss will perform ,is jumping from it's initial postion to directly on players body (Hurting him). Now I am not getting the idea how to set the initial velocity of boss so that it will jump on player's body always. We have two factors Boss position and Player Position (End Point).Any Formula/suggestions will be appreciated. thanks

Answer 1

First the vertical part.

Conventions: up is the positive direction, and g is positive.

To start from A_y and reach maximum height H requires an initial velocity V_y=sqrt(2g(H-A_y)).

The time to reach this height and then fall back down to B_y is t=sqrt(2/g) (sqrt(H-A_y)+sqrt(H-B_y)).

Now we can do the horizontal part. To get from A_x to B_x in the time t, we must have a (constant) horizontal velocity V_x = (B_x-A_x)/t.