# Badminton Net Kill Shot#

In a game of badminton, to counter a weak lift shot, the receiver can orient their racket at certain angle relative to the vertical. Thus, he/she is able to utilize the incoming momentum of the shuttle and principles of oblique impacts to return the shuttle at a steep angle without exerting an additional impulse. This agile shot is termed as a badminton net kill shot due to its play in close proximity to the net.

## Part 1#

Treat the racquet and shuttle as particles with masses $$1\ \rm{kg}$$, $$0.1\ \rm{kg}$$ respectively in a vertical plane. Assume the racquet is stationary before the collision. Neglect aerodynamic drag and effects of gravity at the point of collision.

Calculate the angle($$\alpha$$) with which the racquet has to be oriented relative to the collision to achieve the desired trajectory as shown above.
$$\theta = {{ params.theta }}^{\circ}$$, $$u\_{shuttle} = {{ params.u_s }}\ \rm{m/s}$$ , $$v\_{shuttle} = {{ params.v_s }}\ \rm{m/s}$$, $$h = {{ params.h }}\ \rm{m}$$, $$h\_{net} = 1.524\ \rm{m}$$, $$x = 1.6256\ \rm{m}$$
You may have to use the compound angle identity: $$sin(A \pm B) = sin(A)cos(B) \pm cos(A)sin(B)$$

Please enter in a numeric value in $$\circ$$.

## Part 2#

Determine the the magnitude of the final velocity of the racket. Treat the badminton racket as a rigid body.

Please enter the value of $$v\_{racket}$$ in $$\rm{m/s}$$.

## Part 3#

Determine the coefficient of restitution($$e$$) between the racket and the shuttle.

Please enter the value of $$e$$.