A 1500 kg truck traveling at 80 km/h collides with another car of mass 1000 kg traveling at 30 km/h in the same direction. The two cars stick together after the collision. Their speed immediately after the collision is
a. 40 km/h
b. 60 km/h
c. 110 km/h
d. 55 km/h

The speed of two cars immediately after the collision is 60 km/h. Hence, option (b) is correct.

Given data:

The mass of truck is, M = 1500 kg.

The initial speed of truck is, u = 80 km/h.

The mass of car is, m = 1000 kg.

The initial speed of car is, u' = 30 km/h.

The given problem is based on the conservation of linear momentum, which says that the total momentum before collision is equal to the total momentum after the collision.

As per the conservation of momentum,

Mu + mu =(M + m)v

Here, v is the speed of two cars after the collision.

Solving as,

Thus, we can conclude that the speed of two cars immediately after the collision is 60 km/h. Hence, option (b) is correct.

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b. 60 km/h

Explanation:

Momentum = mass × velocity

Before collision,

Momentum of truck is

1500 × 80 = 120000 kg.km/h

Momentum of car is

1000 × 30 = 30000 kg.km/h

Since they are moving in the same direction, total momentum before collision is

120000 + 30000 = 150000 kg.km/h

After Collision, the two cars stick together after the collision. It means that they have a common velocity, V km/h. Therefore, momentum after collision is

V(1500 + 1000)

= 2500V kg.km/h

The law of conservation of momentum states that the total momentum of two objects before collision = the total momentum of the two objects after collision. Therefore

2500V = 150000

V = 150000/2500

V = 60 km/h