An inelastic collision occurs between a large truck and smaller sedan. Calculate the final velocity of the objects and explain the direction they will be traveling with the following data from before the collision: Small sedan mass = 1300 kg initial velocity = 20 m/s Truck mass = 7100 kg Initial Velocity 15 m/s
momentum is conserved
(7100 * 15) - (1300 * 20) = (7100 + 1300) * v
... in the direction of the truck
To calculate the final velocity of the objects involved in the inelastic collision, we need to apply the principle of conservation of momentum. In an inelastic collision, the objects stick together after the collision and move as a single unit. Therefore, the final velocity will be the same for both the small sedan and the large truck.
The formula for calculating the final velocity in an inelastic collision is:
(m1 * v1) + (m2 * v2) = (m1 + m2) * vf
Where:
m1 = mass of the small sedan
v1 = initial velocity of the small sedan
m2 = mass of the large truck
v2 = initial velocity of the large truck
vf = final velocity of both objects after the collision
Given the data:
m1 = 1300 kg
v1 = 20 m/s
m2 = 7100 kg
v2 = 15 m/s
Plugging these values into the formula:
(1300 kg * 20 m/s) + (7100 kg * 15 m/s) = (1300 kg + 7100 kg) * vf
(26000 kg*m/s) + (106500 kg*m/s) = (8400 kg) * vf
132500 kg * m/s = 8400 kg * vf
Dividing both sides of the equation by 8400 kg, we get:
vf = (132500 kg * m/s) / 8400 kg
vf ≈ 15.77 m/s
So, the final velocity of both the small sedan and the large truck after the collision is approximately 15.77 m/s.
Regarding the direction they will be traveling, since we have not specified any negative signs for the velocities, we will assume positive directions for both. Therefore, both the small sedan and the large truck will be traveling in the same direction after the collision.