Question

Two football players run towards each other along a straight path in Penrith Park in the clash between the Melbourne storms and the Penrith Panthers a month ago. Melbourne's Justin Olam who is about 95kg and ran towards Viliame Kikau at 3.75m/s. Viliame Kikau is 111kg and moves towards Justin Olam at 4.10m/s. They end up in a head-on collision and are stuck together.

A) What is their velocity immediately after the collision?

B) What are the initial and final kinetic energies of the system?​

Answer 1

a) v = 0.4799 m / s, b) K₀ = 1600.92 J, K_f = 5.46 J

Step-by-step explanation:

a) How the two players collide this is a momentum conservation exercise. Let's define a system formed by the two players, so that the forces during the collision are internal and also the system is isolated, so the moment is conserved.

Initial instant. Before the crash

p₀ = m v₁ + M v₂

where m = 95 kg and his velocity is v₁ = -3.75 m / s, the other player's data is M = 111 kg with velocity v₂ = 4.10 m / s, we have selected the direction of this player as positive

Final moment. After the crash

p_f = (m + M) v

as the system is isolated, the moment is preserved

p₀ = p_f

m v₁ + M v₂ = (m + M) v

v =
`(m v_1 + M v_2)/(m+M)`

let's calculate

v =
`( -95 \ 3.75 \ + 111 \ 4.10)/(95+111)`

v = 0.4799 m / s

b) let's find the initial kinetic energy of the system

K₀ = ½ m v1 ^ 2 + ½ M v2 ^ 2

K₀ = ½ 95 3.75 ^ 2 + ½ 111 4.10 ^ 2

K₀ = 1600.92 J

the final kinetic energy

K_f = ½ (m + M) v ^ 2

k_f = ½ (95 + 111) 0.4799 ^ 2

K_f = 5.46 J