1) A 0.5 kg ball moving horizontally at 10.0 m/s strikes a vertical well and rebounds in the opposite direction at 5.0 m/s. If the collision took place in 0.1 s, what was the magnitude of the average force on the wall?

2) You are standing on a sheet of ice that covers the football stadium parking lot in Buffalo, where there is negligible friction between your feet and the ice. A friend throws you a ball of mass 0.500 kg that is traveling horizontally at 10 m/s. Your mass is 65.0 kg. If the ball hits you and bounces off your chest elastically, what is your speed after the collision? 

 

1)

initial momentum is

?Pi?=m1?v1?=0.5×10=5 kgm/s?

Final momentum is

?Pf?=m1?v2?=0.5×−5=−2.5 kgm/s?

time taken for this change in momentum is ?Δt=0.1 s?

impulse is change in momentum

i.e.

?FΔt=Δp=Pf?−Pi?=−2.5−5=−7.5kgm/s?

hence

?F=DeltatΔp?=0.1−7.5?=−75N?

hence magnitude of average force is ?F=75 N?

2)

?m1?=0.500kg?

??v1i?=10m/s?

?v1f?= ??

?m2?=65.0kg?

?v2i?=0?

?v2f?= ??

by conservation of momentum,

??m1?v1i?+m2?v2i?=m1?v1f?+m2?v2f??

?5+0=0.5v1f?+65v2f??

??v1f?+130v2f?=10??

?v1f?=10−130v2f??

now since the collision is elastic, kinetic energy is conserved

i.e.

??21?m1?v1i2?+21?m2?v2i2?=21?m1?v1f2?+21?m2?v2f2??

or

??m1?v1i2?+m2?v2i2?=m1?v1f2?+m2?v2f2??

?0.5×102+0=0.5v1f2?+65v2f2??

?50=0.5(10−130v2f?)2+65v2f2??

??50=50−1300v2f?+16900v2f2?+65v2f2??

?16965v2f2?−1300v2f?=50−50=0?

?16965v2f2?=1300v2f??

?v2f?=169651300?=0.0766m/s?

?v1f?=10−130v2f?=10−130×0.0766=10−9.958=0.042 m/s?

hence the velocity of ball after collision is ?0.042 m/s?

and my velocity after the ball hits me is ??0.0766 m/s?