Question

A car with mass m = 1.20x10�� kg is initially traveling directly east with a speed vi = 25.0 m/s. It crashes into the rear end of a truck with mass m = 9.00x10�� kg moving in the same direction with speed 20.0 m/s. Immediately after the collision, the car has a speed vf = 18.0 m/s in its original direction. What is the velocity of the truck immediately after the collision?

Answer 1

Using the conservation of momentum, the velocity of the truck after the collision can be calculated to be approximately 23.15 m/s toward the east.

Step-by-step explanation:

The question is asking for the velocity of the truck after colliding with a car. To find this, we apply the conservation of momentum principle, which states that the total momentum before the collision is equal to the total momentum after the collision. We can use the following formula:

Total momentum before collision = Total momentum after collision

(mcar × vi,car) + (mtruck × vi,truck) = (mcar × vf,car) + (mtruck × vf,truck)

Let's plug in the given values:

(1.20 × 103 kg × 25.0 m/s) + (9.00 × 103 kg × 20.0 m/s) = (1.20 × 103 kg × 18.0 m/s) + (9.00 × 103 kg × vf,truck)

We can solve for vf,truck to find the truck's velocity after the collision:

(1.20 × 103 kg × 25.0 m/s) + (9.00 × 103 kg × 20.0 m/s) - (1.20 × 103 kg × 18.0 m/s) = 9.00 × 103 kg × vf,truck

30000 + 180000 - 21600 = 9.00 × 103 kg × vf,truck

208400 = 9.00 × 103 kg × vf,truck

vf,truck = 208400 / 9.00 × 103 kg

vf,truck ≈ 23.15 m/s

Therefore, the truck's velocity after the collision is approximately 23.15 m/s in the original direction of east.