Question

for a movie stunt, an empty truck with a mass of 2000 kg goes 10 m/s and runs into a stopped car of mass 1000 kg. the truck then keeps moving and pushes the car along with it. if there are no other forces acting on this system, which best describes the results of the collision? the collision is perfectly elastic. kinetic energy stays the same. the momentum after the collision is greater than the momentum before the collision. the speed of the combined vehicles is less than the initial speed of the truck.

Explanation:

Step1: Identify the type of collision

The truck and car stick together after the collision, so it is an in - elastic collision. In in - elastic collisions, kinetic energy is not conserved.

Step2: Apply the law of conservation of momentum

The law of conservation of momentum states that $p_{before}=p_{after}$, where $p = mv$. Before the collision, $p_{before}=m_{truck}v_{truck}+m_{car}v_{car}$, with $m_{truck} = 2000$ kg, $v_{truck}=10$ m/s, $m_{car}=1000$ kg and $v_{car} = 0$ m/s. So $p_{before}=2000\times10+1000\times0=20000$ kg·m/s. After the collision, $p_{after}=(m_{truck}+m_{car})v_{combined}$, where $m_{truck}+m_{car}=2000 + 1000=3000$ kg. Since $p_{before}=p_{after}$, we have $20000=(2000 + 1000)v_{combined}$, and $v_{combined}=\frac{20000}{3000}=\frac{20}{3}\approx6.67$ m/s which is less than the initial speed of the truck (10 m/s).

Step3: Analyze each option

• A perfectly elastic collision is one where kinetic energy is conserved. Since the vehicles stick together, this is an in - elastic collision, so the first option is wrong.
• Kinetic energy is not conserved in in - elastic collisions, so the second option is wrong.
• By the law of conservation of momentum, $p_{before}=p_{after}$, so the third option is wrong.
• As calculated above, $v_{combined}=\frac{20}{3}$ m/s $< 10$ m/s, so the fourth option is correct.

Answer:

The speed of the combined vehicles is less than the initial speed of the truck.