A ball with a mass of #4 kg # and velocity of #3 m/s# collides with a second ball with a mass of #5 kg# and velocity of # 2 m/s#. If #20%# of the kinetic energy is lost, what are the final velocities of the balls?
Ball 1:
Ball 2:
Collisions can be represented using momentum relations.
Now we can form some equations describing the postcollision system, which we can use to find the velocities of the balls.
It is good that this value is negative, as ball 1 was originally traveling in the positive direction. Postcollision, it should go the opposite direction.
Hence we have found the final velocities of the balls:
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To find the final velocities of the balls after the collision, we can use the principle of conservation of momentum and the equation for kinetic energy.

Conservation of momentum: (m_1v_1 + m_2v_2 = m_1v_{1f} + m_2v_{2f})

Equation for kinetic energy: (KE = \frac{1}{2}mv^2)
Using these equations, we can solve for the final velocities (v_{1f}) and (v_{2f}):
For the first ball: Initial momentum: (4 \times 3 + 5 \times (2) = 12  10 = 2) kg m/s Initial kinetic energy: (\frac{1}{2} \times 4 \times 3^2 = 18) J Final kinetic energy: (0.8 \times 18 = 14.4) J Final velocity: (\sqrt{\frac{2 \times 14.4}{4}} = 1.2) m/s
For the second ball: Initial momentum: (4 \times 3 + 5 \times (2) = 12  10 = 2) kg m/s Initial kinetic energy: (\frac{1}{2} \times 5 \times (2)^2 = 10) J Final kinetic energy: (0.8 \times 10 = 8) J Final velocity: (\sqrt{\frac{2 \times 8}{5}} \approx 0.8) m/s
So, the final velocities of the balls are approximately (1.2 , \text{m/s}) and (0.8 , \text{m/s}) respectively.
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When evaluating a onesided 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.
When evaluating a onesided 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.
When evaluating a onesided 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.
When evaluating a onesided 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.
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