A ball with a mass of # 5 kg# is rolling at #3 m/s# and elastically collides with a resting ball with a mass of #2 kg#. What are the post-collision velocities of the balls?

Answer 1

#v_1=9/7 m/s#
#v_2=30/7 m/s#

#5*3+0=5*v_1+2*v_2# #15=5*v_1+2*v_2" (1)"# #3+v_1=0+v_2" (2)"# #color(red)"'the sum of the velocities of objects before and after collision must be equal'"# #"write " v_2=3+v_1" at (1)"# #15=5*v_1+2*(3+v_1)# #15=5.v_1+6+2*v_1# #15-6=7*v_1# #9=7*v_1# #v_1=9/7 m/s# #use :" (2)"# #3+9/7=v_2# #v_2=30/7 m/s#

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Answer 2

Parker Abbott

Using the conservation of linear momentum and the principles of elastic collisions:

[ m_1 \cdot v_{1i} + m_2 \cdot v_{2i} = m_1 \cdot v_{1f} + m_2 \cdot v_{2f} ]

[ v_{1f} = \frac{(m_1 - m_2) \cdot v_{1i} + 2 \cdot m_2 \cdot v_{2i}}{m_1 + m_2} ]

[ v_{2f} = \frac{2 \cdot m_1 \cdot v_{1i} + (m_2 - m_1) \cdot v_{2i}}{m_1 + m_2} ]

Substitute the given values:

[ v_{1f} = \frac{(5 - 2) \cdot 3 + 2 \cdot 2 \cdot 0}{5 + 2} ]

[ v_{2f} = \frac{2 \cdot 5 \cdot 3 + (2 - 5) \cdot 0}{5 + 2} ]

[ v_{1f} \approx 1.57 \ \text{m/s} ]

[ v_{2f} \approx 2.29 \ \text{m/s} ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.