Two skaters, Elena and Tara, face each other on the ice. Elena has a mass of 57.4 kg, and Tara has a mass of 48.3 kg. Both are motionless until they push away with a force of 33 N. Then Elena has a velocity of 1.4 m/s. What is Tara’s velocity?

-1.7 m/s

-1.7m/s

To find Tara's velocity, we can use the principle of conservation of momentum. According to this principle, the total momentum of an isolated system remains constant before and after an event.

The formula for momentum is given by:
momentum = mass × velocity

First, let's calculate the initial momentum before the skaters push away from each other:

Total initial momentum = Elena's initial momentum + Tara's initial momentum

Since both skaters are motionless initially, their initial momenta are:

Elena's initial momentum = 0
Tara's initial momentum = 0

Therefore, the total initial momentum is also 0.

Now, let's consider the final momentum after the skaters push away from each other. Since momentum is conserved, the total final momentum should also be 0.

Total final momentum = Elena's final momentum + Tara's final momentum

Elena's final momentum = mass of Elena × velocity of Elena
= 57.4 kg × 1.4 m/s

Now, let's find Tara's final momentum using the conservation of momentum principle:

Total final momentum = 0

Therefore,
Tara's final momentum = - (Elena's final momentum)
= - (57.4 kg × 1.4 m/s)

Finally, we can find Tara's velocity by dividing her final momentum by her mass:

Tara's final momentum = mass of Tara × velocity of Tara

Therefore,
velocity of Tara = Tara's final momentum / mass of Tara

Substituting the values, we have:

velocity of Tara = - (57.4 kg × 1.4 m/s) / 48.3 kg

Calculating the values, we get:

velocity of Tara ≈ -1.66 m/s

Since velocity is a vector quantity, the negative sign indicates that Tara is moving in the opposite direction to Elena. Therefore, Tara's velocity is approximately 1.66 m/s in the opposite direction to Elena's velocity.

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