A 2115 kg car moving east at 10.61 m/s col- lides with a 3169 kg car moving north. The cars stick together and move as a unit after the collision, at an angle of 32.4◦ north of east and at a speed of 5.03 m/s.

Question

A 2115 kg car moving east at 10.61 m/s col- lides with a 3169 kg car moving north. The cars stick together and move as a unit after the collision, at an angle of 32.4◦ north of east and at a speed of 5.03 m/s.

What was the speed of the 3169 kg car before the collision?

Answer 1

original east momentum = 2115*10.61

final east momentum
= (2115+3169)*5.03cos32.4

22440 = 5284 * 4.25 v = 22440 v

v =1 m/s

Answer 2

To find the speed of the 3169 kg car before the collision, we can use the principle of conservation of momentum.

The momentum before the collision is equal to the momentum after the collision. Momentum is the product of mass and velocity.

Let's assume the initial velocity of the 3169 kg car is v1 m/s.

The momentum before the collision can be calculated by multiplying the mass and velocity of each car separately:

For the 2115 kg car moving east:
Momentum = (mass of car 1) * (velocity of car 1)
= (2115 kg) * (10.61 m/s)
= 22,449.15 kg·m/s (to two decimal places)

For the 3169 kg car moving north:
Momentum = (mass of car 2) * (velocity of car 2)
= (3169 kg) * (v1 m/s)
= 3169v1 kg·m/s

Now, let's find the momentum after the collision. Since the cars stick together and move as a unit, we can consider them as one combined mass.

Let the mass of the combined cars after the collision be (2115 kg + 3169 kg) = 5284 kg.

The velocity of the combined cars can be split into two components: one along the east direction and one along the north direction. Given that the angle of motion after the collision is 32.4° north of east, we can use trigonometry to find the components of the velocity:

Velocity along the east direction = (combined speed) * cos(angle)
= 5.03 m/s * cos(32.4°)

Velocity along the north direction = (combined speed) * sin(angle)
= 5.03 m/s * sin(32.4°)

Now, let's find the momentum after the collision by multiplying the combined mass and the combined velocity:

Momentum = (mass of combined cars) * (combined speed)
= (5284 kg) * (5.03 m/s)

Now, since momentum is conserved, we can equate the momentum before the collision to the momentum after the collision:

22,449.15 kg·m/s + 3169v1 kg·m/s = (5284 kg) * (5.03 m/s)

Solving this equation will give us the value of v1, which is the speed of the 3169 kg car before the collision.