1. A fisherman is standing on the top of a bridge that is 80 meters high, and th

Question

1. A fisherman is standing on the top of a bridge that is 80 meters high, and throws a sword towards a fish that is jumping 20 meters above the water.

Ps Mass of the sword is 200.00 grams and the mass of the fish is 500 grams.

a) What is the speed of the sword spearing the fish if the swords initial velocity is 6m/s?
b) At what velocity does the spear and fish hit the water?
c) How long does it take for the sword to spear the fish?
d) How long does it take for the fish to hit the water?
e) What is the momentum of the spear and fish when they hit the water?

Explanation / Answer

( a ) v^2 - u^2 = 2as ;

or v^2 - 6^2 = 2 ( - 9.8 ) [ - ( 80 -20 ) ] ;

or v = 34.8137 m /s ;

( b ) the spear hits the fish ; then

M v = ( M+ m ) V ; V is the composite velocity after spear hts the fish ;

V = Mv / ( M + m ) ;

V = - ( 0.2 * 34.8137 ) / ( 0.2 + 0.5 ) ;

V = 9.946 m /s at the time of hitting ;

velocit at bottom = ( 2 g h ) = ( 2 * 9.8 * 20 ) = 19.798 m /s

( c) s = ut + 0.5 at^2 ;

- ( 80 -20 ) = - 6 t + 0.5 * ( -9.8 ) t^2 ;

- 60 = - 6t - 0.5 * 9.8 t^2 ;

or t = 2.9401 s , we reject the negative value of t

( d ) -20 = - 9.946 t + 0.5 ( -9.8 ) t^2 ;

or t = 1.2459 s ; again we reject the negative value ;

( e ) momentum = ( M + m ) * velocity at bottom = ( 0.5 + 0.2 ) * 19.798 = 13.8586 kg m /s

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