A car moving with an initial speed v collides with a second stationary car that is 50.7 percent as massive. After the collision the first car moves in the same direction as before with a speed that is 33.2 percent of the original speed. Calculate the final speed of the second car. Give your answer in units of the initial speed (i.e. as a fraction of v).

Question

A car moving with an initial speed v collides with a second stationary car that is 50.7 percent as massive. After the collision the first car moves in the same direction as before with a speed that is 33.2 percent of the original speed. Calculate the final speed of the second car. Give your answer in units of the initial speed (i.e. as a fraction of v).

Answer 1

To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

Let's denote the initial speed of the first car as v1, and the initial speed of the second car as v2. The mass of the first car is m1, and the mass of the second car is m2.

Initially, the first car is moving with a speed v1, and the second car is stationary, so its initial speed is 0. The total momentum before the collision is given by:

Total momentum before collision = m1 * v1 + m2 * 0 = m1 * v1

After the collision, the direction of motion of the first car remains the same, and its speed becomes 33.2 percent of the original speed (v1). Therefore, the final speed of the first car (v1') is:

v1' = 0.332 * v1

The second car, which was initially stationary, begins to move in the same direction as the first car after the collision. We need to calculate the final speed of the second car (v2').

Using the principle of conservation of momentum, we can write the equation:

m1 * v1 = m1 * v1' + m2 * v2'

Substituting the values we have:

m1 * v1 = m1 * (0.332 * v1) + m2 * v2'

Now, let's substitute the given information into the equation. We know that the second car is 50.7 percent as massive as the first car, so we can write:

m2 = 0.507 * m1

Substituting this into the equation:

m1 * v1 = m1 * (0.332 * v1) + (0.507 * m1) * v2'

Simplifying:

v1 = 0.332 * v1 + 0.507 * v2'

Now we can solve this equation for v2':

v2' = (v1 - 0.332 * v1) / 0.507

Simplifying:

v2' = (0.668 * v1) / 0.507

Therefore, the final speed of the second car (v2') in terms of the initial speed (v1) is:

v2' = 1.317 * v1

So, the final speed of the second car is 1.317 times the initial speed of the first car.