Question

A 79.0-kg fullback running east with a speed of 5.20 m/s is tackled by a 97.0-kg opponent running north with a speed of 3.00 m/s.

(a) Explain why the successful tackle constitutes a perfectly inelastic collision.

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(b) Calculate the velocity of the players immediately after the tackle.

magnitude	m/s
direction	° north of east

(c) Determine the mechanical energy that disappears as a result of the collision.
J

Account for the missing energy.

Answer 1

if there is any energy loss it will be a inelastic collision. collision and after collision they both move together it means it is perfectly inelastic collision where object sticks and move together.

to calculate velocity we need to apply momentum conservation

in  east

Pi = Pf

79*5.2 = ( 79+97) *V_east

V_east =79*5.2/( 79+97) = 2.33409091 m/s  

momentum conservation in north

Pi = Pf

97*3 = ( 79+97) *V_north

V_north = 97*3/( 79+97) =1.65340909 m/s

magnitude = sqrt( V_east ^2 +V_north ^2) = sqrt(2.33409091^2+1.65340909^2) =

= 2.86 m/s answer  

direction => tan^-1(1.65340909/2.33409091) =35.31° answer

energy loss

KE final -KE initial  

1/2*( 79+97)*2.86^2 - [ 1/2*79*5.2^2 + 1/2*97*3^2 ]

= -784.7752 J

missing energy.

because it is lost in heat and shape change of player ( injury etc )

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