Question

An 89.0 kg fullback moving east with a speed of 5.6 m/s is tackled by an 85.0 kg opponent running west at 2.84 m/s, and the collision is perfectly inelastic.
(a) Calculate the velocity of the players just after the tackle. m/s
(b) Calculate the decrease in kinetic energy during the collision. J
(c) determine the mechanical energy that is lost as a result of the collision.
(d) Where did the lost energy go?

Answer 1

Answer:

a. $v_f=1.477m/s$

b. Δ$K=1558.3J$

c. $E_k=1034.7 J$

Explanation:

a).

Momentum conserved

$p_{ix}=p_{fx}$

$m_1*v_1+m_2*v_2=(m_1+m_2)*v_f$

$v_f=\frac{m_1*v_1+m_2*v_2}{m_1+m_2}$

$v_f=\frac{89.0kg*5.6m/s+85.0kg*-2.84m/s}{(89.0+85.0)kg}$

$v_f=1.477m/s$

b).

Δ$K=K_i-K_f$

$\frac{1}{2}*m_1*v_1^2+\frac{1}{2}*m_2*v_2^2=\frac{1}{2}*(m_1+m_2)*v_f^2$

$\frac{1}{2}*89.0kg*(5.6m/s)^2+\frac{1}{2}*85.0kg*(2.84m/s)^2=\frac{1}{2}*(89.0+85.0)kg*(1.447m/s)^2$

Δ$K=1558.3J$

c).

$E_k=\frac{1}{2}*89kg*(5.8m/s)^2-\frac{1}{2}*(85+89)kg*(1.44m/s)^2$

$E_k=1034.7 J$

d).

All of which has been lost as mechanical energy, and is now thermal energy warmer football players, noise a loud crunch for example.