Question

A 89.5-kg fullback running east with a speed of 5.05 m/s is tackled by a 95.5-kg opponent running north with a speed of 3.10 m/s.

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

(b) Calculate the velocity of the players immediately after the tackle (I HAVE THE ANSWER TO B)

magnitude: 2.91 ?direction: 33.25	m/s north of east

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

Account for the missing energy. (explain)

Answer 1

here,

for m1 = 89.5 kg is at u1 = 5.05 m/s i

for m2 = 95.5 kg is at u2 = 3.1 m/s j

a)

for the successful tackle

the collison must be perfectly inelastic

because the players must be stick together

b)

let the final speed be v

using conservation of momentum

m1 * u1 + m2 * u2 = (m1 + m2) * v

89.5 * 5.05 i + 95.5 * 3.1 j = ( 89.5 + 95.5) * v

solving for v

v = 2.44 i + 1.6 j m/s

magnitude , |v| = sqrt(2.44^2 + 1.6^2)

|v| = 2.91 m/s

theta = arctan(1.6/2.44) = 33.25 degree north of east

c)

the mechanical energy that disappears as a result of the collision , ME = 0.5 * m1 * u1^2 + 0.5 * m2 * u2^2 - 0.5 * (m1+ m2) * u^2

ME = 0.5 * 89.5 * 5.05^2 + 0.5 * 95.5 * 3.1^2 - 0.5 * (89.5 + 95.5) * 2.91^2 J

ME = 816.8 J

the mechanical energy is converted into heat energy