a 10000 kg truck moving at 10 m/s collides with a 2000 kg car moving at 30 m/s in the opposite direction. If they stick together after impact how fast, and in what direction, will they be moving?
To find the velocity of the truck and car after the collision, we will use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity. Therefore, we can write the equation:
(mass of truck * velocity of truck) + (mass of car * velocity of car) = (total mass * final velocity)
Plugging in the given values:
(10000 kg * 10 m/s) + (2000 kg * (-30 m/s)) = (10000 kg + 2000 kg) * final velocity
100000 kg*m/s - 60000 kg*m/s = 12000 kg * final velocity
40000 kg*m/s = 12000 kg * final velocity
Now, we can solve for the final velocity:
final velocity = 40000 kg*m/s / 12000 kg
final velocity = 3.33 m/s
Since the final velocity is positive, the truck and car will be moving in the forward direction after the collision.
Therefore, the truck and car will be moving together at a speed of 3.33 m/s in the forward direction.
To solve this problem, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Momentum (p) is calculated by multiplying the mass (m) of an object by its velocity (v):
Momentum = Mass x Velocity
Before the collision, the momentum of the truck is given by:
Momentum of truck before collision = (mass of truck) x (velocity of truck)
= (10000 kg) x (10 m/s)
= 100,000 kg*m/s
The momentum of the car is given by:
Momentum of car before collision = (mass of car) x (velocity of car)
= (2000 kg) x (30 m/s)
= 60,000 kg*m/s
Since the car is moving in the opposite direction, we consider its velocity as negative.
Now, let's calculate the total momentum before the collision:
Total momentum before collision = Momentum of truck before collision + Momentum of car before collision
= 100,000 kg*m/s + (-60,000 kg*m/s)
= 40,000 kg*m/s
After the collision, the two vehicles stick together, so we have a combined system with a total mass of:
Total mass = mass of truck + mass of car
= 10000 kg + 2000 kg
= 12000 kg
Now, let's find the velocity of the combined system after the collision.
Total momentum after collision = Total mass x Velocity of combined system
40,000 kg*m/s = 12000 kg x Velocity of combined system
Now, we can solve for the velocity of the combined system:
Velocity of combined system = 40,000 kg*m/s / 12000 kg
Velocity of combined system ≈ 3.33 m/s
The positive sign of the velocity indicates that the combined system moves in the same direction as the truck before the collision. Therefore, the truck and car will be moving together at a speed of approximately 3.33 m/s in the direction of the truck's initial velocity.