Question

A truck of mass 2500 kg moving at 15 m/s collides with a car of mass 1000 kg moving at 5 m/s in the opposite direction. With what velocity would the two move together?

Answer 1

Given :

• Mass of truck = 2500 kg
• Speed of Truck = 15m/s
• Mass of car = 1000 kg
• Speed of car = 5m/s

To Find :

The common Speed of both vehicles after collision.

Law to be applied:

We will here apply the law of conservation of momentum. In this law , it is stated that the momentum of all the objects are always conserved . It just transfers from one to another .

This law states:

• M1U1+M2U2 = M1V2+M2V2

here, M1 = mass of truck

M2 = mass of car

V1, V2 = Final Velocity of vehicles

U1, U2 = initial velocity of vehicles

Process :

We will first find the initial momentum of both vehicles, then form an equation according to this law, then we will try to solve the equation to get the final velocity of both vehicles.

Note: Here, The car is travelling in opposite direction, hence, its initial momentum will be taken in negative.

Solution :

given, Mass of Truck = 2500 kg

Mass of car = 1000 kg

Initial velocity of Truck = 15m/s

Initial velocity of Car = -5 m/s

Hence , initial momentum of both vehicles:

M1U1+M2U2

= (2500×15)+(1000×(-5))

= 37500-5000

= 32500

Now, let the final velocity of both vehicles be 'x'

So, final momentum of both vehicles:

M2V2+M1V1

= (1000×x)+(2500×x)

= 1000x+2500x

= 3500x

As stated in the law, The final momentum = initial momentum of the vehicles,

Hence,

3500x = 32,500

$\tt{ \implies \: x = \frac{32500}{3500} }$

$\implies \tt{ x \approx 9.2855}$

Hence, Final velocity ≈ 9.2855 m/s

Answer 2

I dunno the explanation but the answer is:

Final velocity = 9.3 m/s