Question

After collision, the car sticks together and moves at an angle of 32 degrees with a velocity of 18 m/s. What was the initial velocity of the car before the collision?

1) 12 m/s
2) 15 m/s
3) 20 m/s
4) 24 m/s

Answer 1

In an elastic collision, the total momentum before the collision is equal to the total momentum after the collision. Therefore, we can use the conservation of momentum to find the initial velocity of the car. The final velocity of the car after the collision can be calculated using trigonometry and the given angle. We can then solve for the initial velocity of the car using these equations.

Step-by-step explanation:

In an elastic collision, the total momentum before the collision is equal to the total momentum after the collision. Therefore, we can use the conservation of momentum to find the initial velocity of the car.

Let's assume that the initial velocity of the car before the collision is 'v' m/s.

The momentum before the collision is the sum of the momentum of the car and the momentum of the object it collides with.

Momentum before collision = (mass of car) × (initial velocity of car) + (mass of object) × (initial velocity of object)

Since the car sticks together after the collision, their final velocity will be the same. We can use trigonometry to calculate the final velocity of the car after the collision.

In this case, the angle of 32 degrees refers to the angle between the final velocity vector of the car and the initial velocity vector of the car. We can use the cosine of this angle to find the magnitude of the final velocity of the car.

Final velocity of the car = (magnitude of final velocity) × (cos(32 degrees))

Using the given information, we can now solve for the initial velocity of the car.