Find the forces on each driver assuming the following data: each driver's mass is 80kg, the total mass of the car and its driver is 700kg, the total mass of the truck and its driver is 4300kg, and they begin by moving directly toward each other, each at 12 m/s. The collision lasts 0.85 seconds. Take the positive direction to be the truck's direction, so that V₁ = +12 m/s and v₂i = -12 m/s. Hint: first determine the final velocity of the car & truck stuck together.

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**Educational Text: Understanding Forces in a Head-On Collision**

**Scenario Description:**

In a head-on collision between a truck (object #1) and a car (object #2), surprisingly, the force exerted by the truck on the car is equal in magnitude and opposite in direction to the force exerted by the car on the truck. Due to their differing masses, the outcomes for both vehicles are quite different: the truck tends to continue moving forward, while the car is significantly damaged and attaches to the front of the truck.

Additionally, the force felt by each driver (assuming each is safely buckled in) varies. The force the car exerts on its driver is distinct from the force the truck exerts on its driver, as they are separate interactions.

**Problem Statement:**

Calculate the forces on each driver using the following data: 

- Each driver's mass = 80 kg
- Total mass of the car and its driver = 700 kg
- Total mass of the truck and its driver = 4300 kg

Both vehicles are moving directly towards each other at 12 m/s. The collision duration is 0.85 seconds. Assume the truck's direction is positive, with initial velocities:
- \( v_{1i} = +12 \) m/s (truck)
- \( v_{2i} = -12 \) m/s (car)

**Hint:** Begin by determining the final velocity of the car and truck stuck together after the collision.
Transcribed Image Text:**Educational Text: Understanding Forces in a Head-On Collision** **Scenario Description:** In a head-on collision between a truck (object #1) and a car (object #2), surprisingly, the force exerted by the truck on the car is equal in magnitude and opposite in direction to the force exerted by the car on the truck. Due to their differing masses, the outcomes for both vehicles are quite different: the truck tends to continue moving forward, while the car is significantly damaged and attaches to the front of the truck. Additionally, the force felt by each driver (assuming each is safely buckled in) varies. The force the car exerts on its driver is distinct from the force the truck exerts on its driver, as they are separate interactions. **Problem Statement:** Calculate the forces on each driver using the following data: - Each driver's mass = 80 kg - Total mass of the car and its driver = 700 kg - Total mass of the truck and its driver = 4300 kg Both vehicles are moving directly towards each other at 12 m/s. The collision duration is 0.85 seconds. Assume the truck's direction is positive, with initial velocities: - \( v_{1i} = +12 \) m/s (truck) - \( v_{2i} = -12 \) m/s (car) **Hint:** Begin by determining the final velocity of the car and truck stuck together after the collision.
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