Exercise 8.27 Two ice skaters, Daniel mass 60.0 kg) and Rebecca (mass 45.0 kg),

Question

Exercise 8.27 Two ice skaters, Daniel mass 60.0 kg) and Rebecca (mass 45.0 kg), are practicing. Daniel stops to tie his shoelace and, while at rest, is struck by Rebecca, who is moving at 13.0 m/s before she collides with him. After the collision, Rebecca has a velocity of magnitude 6.00 m/s at an angle of 53.1 from her initial direction. Both skaters move on the frictionless, horizontal surface of the rink Part A What is the magnitude of Daniel's velocity after the collision? m/S Submit My Answers Give Up incorrect; Try Again; 5 attempts remaining Part B What is the direction of Daniel's velocity after the collision? o from the Rebecca's original direction Submit My Answers Give Up

Explanation / Answer

consider i and j be unit vectors along +ve x and +ve y axis.

let initial direction of rebecca's velocity be along +ve x axis.

then her velocity in vector notation=u1=(13 m/s) i

her velocity after collision=v1=6*(cos(53.1) i + sin(53.1) j)=3.6 i +4.8 j m/s

let daniel's x component is Vx and y component is Vy.

conserving momentum :

mass of daniel * initial velocity of daniel + mass of rebecca * initial velocity of rebecca = mass of daniel * final velocity of daneil + mass of rebecca * final velocity of rebecca

==>60*0+45*(13 i)=60*(Vx i + Vy j)+45*(3.6 i +4.8 j)

equating x and y components,

45*13=60*vx+45*3.6

==>Vx=7.05 m/s

and 60*Vy+45*4.8=0

==>Vy=-3.6 m/s

so magnitude of daniel's velocity after collsion=sqrt(Vx^2+Vy^2)=7.916 m/s

part B:

angle with +ve x axis=arctan(Vy/Vx)=-23.463 degrees

part C:

change in total kinetic energy=final kinetic energy - initial kinetic energy

=0.5*60*7.916^2+0.5*45*6^2-0.5*45*13^2

=-1112.6 J

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