Question

A ball of mass 0.440 kg moving east (+x direction) with a speed of 3.80 m/s collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?

Answer 1

Answer:

The speed and direction of each ball after the collision is  1.27 m/s to East direction and  5.07 m/s to East direction.

Explanation:

given information

m₁ = 0.440 kg

v₁ = 3.80 m/s

m₂ = 0.220 kg

v₂ = 0

collision is perfectly elastic

v₁ - v₂ = - (v₁'- v₂')

v₁ =  - (v₁'- v₂')

v₂' = v₁ + v₁'

according to momentum conservation energy

m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'

m₁v₁  = m₁v₁' + m₂(v₁ + v₁')

m₁v₁  =  m₁v₁' + m₂v₁ + m₂v₁'

m₁v₁ - m₂v₁ = m₁v₁' + m₂v₁'

v₁ (m₁ - m₂) = (m₁ + m₂) v₁'

v₁' = (m₁ - m₂)v₁ / (m₁ + m₂)

    = (0.440 - 0.220) (3.8) / (0.440 + 0.220)

     = 1.27 m/s to East direction

v₂' = v₁ + v₁'

    = 3.8 + 1.27

= 5.07 m/s to East direction

Answer 2

The final velocity of the first ball is 1.267 m/s in positive x-direction and the final velocity of the second object is 5.1 m/s in the positive x-direction.

The given parameters;

• mass of the ball, m = 0.44 kg
• speed of the ball, u = 3.8 m/s
• mass of the second ball, m₂ = 0.22 kg
• initial velocity of the second ball, u₂ = 0

The velocity of each ball after collision is calculated by applying the principle of conservation of linear momentum;

$m_1u_1 + m_2 u_2 = m_1v_1 + m_2 v_2\\\\0.44(3.8) \ + \ 0.22(0) = 0.44v_1 + 0.22v_2\\\\1.672 = 0.44v_1 + 0.22v_2$

Apply one-dimensional linear velocity;

$u_1 + v_1 = u_2 + v_2\\\\3.8 + v_1 = 0 + v_2\\\\v_2 = 3.8 + v_1$

substitute the value of v₂ into the first equation;

$1.672 = 0.44v_1 \ + \ 0.22(3.8 + v_1)\\\\1.672 = 0.44v_1 + 0.836 \ + \ 0.22v_1\\\\0.836 = 0.66v_1\\\\v_1 = \frac{0.836}{0.66} \\\\v_1 = 1.267 \ m/s$

The final velocity of the second object is calculated as;

$v_2 = 3.8 + v_1\\\\v_2 = 3.8 + 1.267\\\\v_2 = 5.1 \ m/s$

Thus, the final velocity of the first ball is 1.267 m/s in positive x-direction and the final velocity of the second object is 5.1 m/s in the positive x-direction.

Learn more here:https://brainly.com/question/24424291