Answered: A1500 kg car moving at 8 m/s to…

A1500 kg car moving at 8 m/s to theright strikes a 1000 kg car moving to the left. If the cars stick together and stop moving right after the collision, find the initial velocity of the 1000 kg car.

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Question

A1500 kg car moving at 8 m/s to theright strikes a 1000 kg car moving to the left. If the cars
stick togetherand stop moving right after the collision, find the initial velocity of the 1000 kg
car.

Expert Solution

Step 1

Given:

The mass of first car is $m_{1} = 1500 kg$ .
The initial speed of first car is $u_{1} = 8 m / s$ .
The mass of second car is $m_{2} = 1000 kg$ .
The final velocity of both the cars is $v = 0 m / s$ .

The formula to calculate the initial momentum of the system is,

$p_{i} = m_{1} u_{1} + m_{2} u_{2}$

Here, p_i is the initial momentum, m₁ is the mass of first car, u₁ is the initial velocity of first car, m₂ is the mass of second car and u₂ is the initial velocity of second car.

The formula to calculate the final momentum of the system is,

$p_{f} = (m_{1} + m_{2}) v$

Here, p_f is the final momentum and v is the final speed of both the cars.

According to conservation of linear momentum,

$p_{i} = p_{f}$