At a crossing a truck travelling towards the north collides with a car

Question

At a crossing a truck travelling towards the north collides with a car travelling towards the east. After the collision the car and the truck stick together and move off at an angle of 30° east of north. If the speed of the car before the collision was 20 ms, and the mass of the truck is twice the mass of the car, calculate the speed of the truck before and after the collision.

22 Jan 2025

Answer :

Word Count : 569

To solve this problem, we can apply the principles of conservation of momentum and energy in the context of elementary mechanics. Since the collision is described as inelastic (the truck and the car stick together after the collision), the conservation of momentum is the key principle we'll rely on.

### Step 1: Define Variables

Let the mass of the car be \( m_c \) and the mass of the truck be \( m_t \). It is given that the mass of the truck is twice the mass of the car, so:

\[
m_t = 2m_c
\]

Let the velocity of the car before the collision be \( v_c = 20 \, \text{m/s} \) towards the east. Let the velocity of the truck before the collision be \( v_t \) towards the north.

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