A 85-kg halfback on a footbal team runs head-on into a 120-kg opponent at an ins

Question

A 85-kg halfback on a footbal team runs head-on into a 120-kg opponent at an instant when neither has his feet on the ground. The halfback is initially going west at 10 m/s , and his opponent is initially going east at 4.37 m/s. The collision is totally inelastic. Suppose that the positive x axis is directed to the west.

A)

If the collision takes 0.247 s , what are the xcomponents of the accelerations of each player?

Part B

How much kinetic energy is converted to incoherent energy during the collision?

Explanation / Answer

let

m1 = 85 kg, v1x = 10 m/s

m2 = 120 kg, v2x = -4.37 m/s

let Vfx is the final velocity.

Apply conservation of momentum

m1*v1x + m2*v2x = (m1+m2)*Vfx

Vfx = (m1*v1x + m2*v2x)/(m1+m2)

= (85*10 + 120*(-4.37))/(85+120)

= 1.59 m/s

acceleration of halfback = (vfx - v1x)/t

= (1.59 - 10)/0.247

= -34 m/s^2 <<<<<<<<<-------------Answer

acceleration of his apponent = (vfx - v2x)/t

= (1.59 - (-4.37))/0.247

= 24.1 m/s^2 <<<<<<<<<-------------Answer

B)delta_KE = 0.5*m1*v1x^2 + 0.5*m2*v2x^2 - 0.5*(m1+m2)*Vfx^2

= 0.5*85*10^2 + 0.5*120*4.37^2 - 0.5*(85+120)*1.59^2

= 5137 J <<<<<<<<<-------------Answer

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