Question

1. A 1700-kg car traveling east at 18 m/s collides with a moving 2500-kg truck.

After they collide, the two interlock and move together with a velocity of 30 m/s
west. What was the original velocity of the truck?

Answer 1

The original velocity of the truck was -62.64 m/s (westward).

Step-by-step explanation:

To solve this problem, we can use the principle of conservation of momentum. The total momentum of an isolated system before a collision is equal to the total momentum after the collision. In this case, the car and truck collide and stick together, so we can set up an equation using the principle of conservation of momentum:

Initial momentum of car + Initial momentum of truck = Final momentum of car and truck

Since the car is traveling east, its initial momentum is its mass multiplied by its velocity: 1700 kg x 18 m/s = 30600 kg·m/s. Similarly, the truck's initial momentum is 2500 kg x V (unknown velocity). After the collision, the car and truck move together with a velocity of 30 m/s west, so their final momentum is the combined mass (1700 kg + 2500 kg) multiplied by the final velocity: 4200 kg x (-30 m/s) = -126000 kg·m/s (the negative sign indicates westward direction).

Setting up the equation:

30600 kg·m/s + 2500 kg x V = -126000 kg·m/s

Simplifying the equation:

2500 kg x V = -156600 kg·m/s

Dividing both sides of the equation by 2500 kg:

V = -156600 kg·m/s ÷ 2500 kg

V = -62.64 m/s

Therefore, the original velocity of the truck was -62.64 m/s (westward).

Answer 2

The speed of the truck is 62.64 m/s towards west

Step-by-step explanation:

As we know that there is no external force on the system of car and truck

so we can say that total momentum of the system must be conserved

so we will have

`m_1v_1 + m_2v_2 = (m_1 + m_2)v`

here we know that

`m_1 = 1700 kg`

`m_2 = 2500 kg`

`v_1 = 18 m/s`

`v_2 = ?`

`v = -30 m/s`

now we have

`1700(18) + 2500 v = (1700 + 2500)(-30)`

`v = 62.64 m/s` Towards West