Question

12.Two ice skaters are initially at rest. The 78.2 kg male ice skater pushes his 48.5 kg female partner forward and away from his body with a velocity of 8.46 m/s. What is the male skater's velocity as a result of the push

Answer 1

Answer:

-5.247 m/s

Explanation:

From the law of conservation of momentum,

Total momentum before collision = Total momentum after collision

Note: Since both ice skaters were initially at rest, therefore the total momentum before collision = 0

0 = mv+m'v'

-mv = m'v'.................... Equation 1

Where m = mass of the male skater, m' = mass of the female skater, v = Final velocity of the male skater, v' = final velocity of the female skater

make v the subject of the equation

v = -(m'v'/m)................ Equation 2

Given: m = 78.2 kg, m' = 48.5 kg, v' = 8.46 m/s

Substitute into equation 2

v = -(48.5×8.46/78.2)

v = -5.247 m/s.

Hence the velocity of the male skater = -5.247 m/s.

Note: The negative sign means that the direction of the velocity of the male skater is in opposite direction to that of the velocity of the female skater

Answer 2

The male skater's velocity as a result of the push is -5.25m/s.

The negative sign shows that he is moving 5.25m/s in the opposite direction.

Given the data in the question;

• Mass of male; $m_1 = 78.2kg$

• Mass of female; $m_2 = 48.5kg$

• Velocity of the male; $v_1 = \ ?$

• Velocity of the female; $V_2 = 8.46m/s$

To determine the male skater's velocity as a result of the push, we use conservation of liner momentum:

$m_1 v_1 + m_2v_2 = 0\\\\or\\\\m_1v_1 = -(m_2v_2)$

Where $m_1$ is mass of male, $m_2$ is mass of female, $v_1$ is the velocity of the male and $v_2$ is the velocity of the female.

We substitute our given values into the equation;

$78.2kg \ *\ v_1 = -( 48.5kg\ *\ 8.46m/s)\\\\v_1 = \frac{-( 48.5kg\ *\ 8.46m/s)}{78.2kg} \\\\v_1 = \frac{-410.31kgm/s}{78.2kg}\\\\v_1 = - 5.25m/s$

{ negative sign shows that it is in opposite direction }

Therefore,  the male skater's velocity as a result of the push is -5.25m/s.

The negative sign shows that he is moving 5.25m/s in the opposite direction.

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