# Impulses, impulses everywhere...

Suppose a ball has been thrown at a wall at a speed 'u' from a height 'H' horizontally (parallel to the ground)

It is rotating at an angular velocity of $$w\sqrt { 2 }$$ in a plane making 45 degrees with the plane in which it was translating initially.

The wall is at a distance $$D$$ from the launch point,

such that

1) $${ 2u }^{ 2 }H<{ D }^{ 2 }g$$

2) $$D\quad <\quad u\sqrt { \frac { 2H }{ g } } +\frac { sin(2\quad arctan(\sqrt { \frac { gH }{ 2 } } ) }{ g }$$

Let the friction on the floor be sufficiently high to just stop rotation (See Note)

Find the average force it exerts on the wall when it collides with the wall provided the impact lasts for 2 seconds and it is perfectly elastic

input the square of a to the closest integer (if it is not an integer)

DETAILS AND ASSUMPTIONS

1) u (initial velocity)=0.7320 approximate as (root(3)-1)

2)w (initial angular velocity)=2.5

4)Mass of Ball=1

All in S.I unit

NOTE

1) the inequalities are not the exact necessary conditions example,, if the question requires a<b then i may have altered it as a<b-1 because the second inequality naturally implies the first one,, so as to not reveal the answer,

2) also the figure shows a satelite view of the problem

3) Considering the balls rotation as a vector superposition of angular velocities along different axes might help

This problem was inspired by Let's play cricket

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