Ms. Burns is driving a 3,116 kg van and is late to her hockey match. She is texting her coach when she slams into a stationary 1,849 kg car. After the inelastic collision, the cars are moving at 6.4 m/s. How fast was Ms. Burns driving?

To find the speed at which Ms. Burns was driving before the collision, we use the conservation of momentum. The van's initial speed was calculated to be 10.20 m/s using the formula derived from the law of conservation of momentum for an inelastic collision.

Explanation:

The subject of the question is Physics, specifically concerning the principles of momentum and collisions. According to the law of conservation of momentum, the total momentum before a collision is equal to the total momentum after the collision in an isolated system. To solve the problem involving Ms. Burns' van colliding with a stationary car, we need to apply this principle.

In an inelastic collision, where the two vehicles stick together after the collision, the combined mass after the collision can be represented as (M1 + M2)Vf where M1 is the mass of Ms. Burn's van, M2 is the mass of the stationary car, and Vf is the final velocity of the combined mass post-collision.

The initial momentum of Ms. Burns' van can be represented as M1Vi, where Vi is the initial velocity we are trying to determine. Because the other car is stationary, its initial velocity is 0 and therefore its initial momentum is also 0.

Now we set up the equation based on the law of conservation of momentum:

M1Vi + M2(0) = (M1 + M2)Vf

Solve for Vi:

Vi = (M1 + M2)Vf / M1

Plugging the values in:

Vi = (3116 kg + 1849 kg)(6.4 m/s) / 3116 kg

Vi = (4965 kg)(6.4 m/s) / 3116 kg

Vi = 31776 kg·m/s / 3116 kg

Vi = 10.20 m/s

Therefore, Ms. Burns was driving at a speed of 10.20 m/s before the collision.