A ball with a mass of $4 k g$ $4 kg$ and velocity of $1 \frac{m}{s}$ $1 m/s$ collides with a second ball with a mass of $5 k g$ $5 kg$ and velocity of $- 8 \frac{m}{s}$ $- 8 m/s$ . If $25 %$ $25%$ of the kinetic energy is lost, what are the final velocities of the balls?

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A ball with a mass of $4 k g$ $4 kg$ and velocity of $1 \frac{m}{s}$ $1 m/s$ collides with a second ball with a mass of $5 k g$ $5 kg$ and velocity of $- 8 \frac{m}{s}$ $- 8 m/s$ . If $25 %$ $25%$ of the kinetic energy is lost, what are the final velocities of the balls?

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Answer 1 · 2017-03-28T10:03:47

Approximately 5.20 meters per second

Explanation:

Kinetic energy formula is $E = 0.5 \cdot m \cdot v \cdot v$ $E= 0.5*m*v*v$
m is for mass (kg) and v is for velocity (m/s).
The first ball's kinetic energy is $E 1 = 2 k g \cdot m \cdot \frac{m}{s \cdot s}$ $E1=2 kg*m*m/(s*s)$
The second ball's kinetic energy is $E 2 = 160 k g \cdot m \cdot \frac{m}{s \cdot s}$ $E2=160 kg*m*m/(s*s)$
Total energy when they collide is $E = 162 k g \cdot m \cdot \frac{m}{s \cdot s}$ $E=162 kg*m*m/(s*s)$

However only 75% of this value is saved after collision of these balls. In other words total kinetic energy after collision is $121.5 k g \cdot m \cdot \frac{m}{s \cdot s}$ $121.5 kg*m*m/(s*s)$

Final mass of these balls $9 k g$ $9 kg$ but what is final velocity?

$121.5 k g \cdot m \cdot \frac{m}{s \cdot s} = 0.5 \cdot 9 \cdot v \cdot v$ $121.5 kg*m*m/(s*s) = 0.5*9*v*v$

$27 = v \cdot v$ $27 = v*v$

$5.196 = v$ $5.196 = v$ (as m/s).

This is the answer of the velocity of the final ball (9 kg). It moves similar to the direction of the second ball with a lower speed.

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A ball with a mass of $4 k g$ $4 kg$ and velocity of $1 \frac{m}{s}$ $1 m/s$ collides with a second ball with a mass of $5 k g$ $5 kg$ and velocity of $- 8 \frac{m}{s}$ $- 8 m/s$ . If $25 %$ $25%$ of the kinetic energy is lost, what are the final velocities of the balls?

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Explanation:

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A ball with a mass of 4kg4 kg and velocity of 1ms1 m/s collides with a second ball with a mass of 5kg5 kg and velocity of −8ms- 8 m/s. If 25%25% of the kinetic energy is lost, what are the final velocities of the balls?

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Explanation:

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A ball with a mass of $4 k g$ $4 kg$ and velocity of $1 \frac{m}{s}$ $1 m/s$ collides with a second ball with a mass of $5 k g$ $5 kg$ and velocity of $- 8 \frac{m}{s}$ $- 8 m/s$ . If $25 %$ $25%$ of the kinetic energy is lost, what are the final velocities of the balls?