Question

You have arrived at the scene of a two car accident. You know the following pieces of information:

Answer 1

The initial velocity of car 1 is 20 m/s to the right

The initial velocity of car 2 is zero

The final velocity of car 2 is 10 m/s to the right

Explanation:

We can solve the problem by using the law of conservation of momentum: the total momentum of the system must be conserved before and after the collision.

Therefore, we can write:

$p_i = p_f\\m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$

where:

$m_1 = 2000 kg$ is the mass of the first car

$u_1$ is the initial velocity of the first car

$v_1 = 10 m/s$ is the final velocity of the first car (taking right as positive direction)

$m_2 = 2000 kg$ is the mass of the second car

$u_2 = 0$ is the initial velocity of the second car

$v_2$ is the final velocity of the second car

We also know the initial momentum of car 1, which is

$p_1 =40,000 kg m/s$

And since momentum is the mass times the velocity, we find the initial velocity of car 1:

$u_1 = \frac{p_1}{m_1}=\frac{40,000}{2,000}=20 m/s$

with a positive sign, since the direction is to the right.

Now we can re-arrange the previous equation and solve for v2, the final velocity of car 2:

$v_2 = \frac{m_1 u_1 -m_1 v_1}{m_2} = \frac{(2000)(20)-(2000)(10)}{2000}=10 m/s$

And since the sign is positive, the direction is the same as the initial direction of car 1, so to the right.

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