A 3000-kg truck moving with a velocity of 10 m/s hits a 1000-kg parked car. The impact causes the 1000-kg car to be set in motion at 15 m/s.
Assuming that momentum is conserved during the collision, determine the velocity of the truck immediately after the collision.
3000*10 = 3000v + 1000*15
5 m/s
To determine the velocity of the truck immediately after the collision, we can 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, the momentum of the truck before the collision is:
Momentum of truck before collision = mass of truck x velocity of truck
= 3000 kg x 10 m/s
= 30000 kg·m/s
The momentum of the car before the collision is:
Momentum of car before collision = mass of car x velocity of car
= 1000 kg x 0 m/s (since the car is parked)
= 0 kg·m/s
The total momentum before the collision is the sum of the momenta of the truck and car:
Total momentum before collision = Momentum of truck before collision + Momentum of car before collision
= 30000 kg·m/s + 0 kg·m/s
= 30000 kg·m/s
According to the principle of conservation of momentum, the total momentum after the collision is also 30000 kg·m/s.
The momentum of the car after the collision is:
Momentum of car after collision = mass of car x velocity of car after collision
= 1000 kg x 15 m/s
= 15000 kg·m/s
Since the total momentum after the collision is equal to the total momentum before the collision, we can calculate the momentum of the truck after the collision:
Total momentum after collision = Momentum of truck after collision + Momentum of car after collision
Rearranging the equation, we can solve for the momentum of the truck after the collision:
Momentum of truck after collision = Total momentum after collision - Momentum of car after collision
= 30000 kg·m/s - 15000 kg·m/s
= 15000 kg·m/s
Now, we can calculate the velocity of the truck after the collision using the equation:
Momentum = mass x velocity
Therefore,
Momentum of truck after collision = mass of truck x velocity of truck after collision
Rearranging the equation, we can solve for the velocity of the truck after the collision:
Velocity of truck after collision = Momentum of truck after collision / mass of truck
= 15000 kg·m/s / 3000 kg
= 5 m/s
Therefore, the velocity of the truck immediately after the collision is 5 m/s.
To solve this problem, we can 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. Mathematically, momentum (p) is expressed as:
p = m * v
Where:
p = momentum
m = mass
v = velocity
Let's calculate the momentum before the collision for both the truck and the car.
Momentum of the truck before the collision:
p(truck) = m(truck) * v(truck)
= 3000 kg * 10 m/s
= 30000 kg m/s
Momentum of the car before the collision:
p(car) = m(car) * v(car)
= 1000 kg * 0 m/s (since the car is parked)
= 0 kg m/s
According to the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision:
p(before collision) = p(after collision)
30000 kg m/s + 0 kg m/s = p(truck) + p(car)
Since the truck's momentum after the collision is not known, we'll call it p(final truck). The momentum of the car after the collision is given as 1000 kg * 15 m/s.
30000 kg m/s = p(final truck) + (1000 kg * 15 m/s)
Now, let's solve for the final momentum of the truck:
p(final truck) = 30000 kg m/s - (1000 kg * 15 m/s)
= 30000 kg m/s - 15000 kg m/s
= 15000 kg m/s
Finally, we can find the velocity (v(final truck)) of the truck immediately after the collision by dividing the final momentum of the truck by its mass:
v(final truck) = p(final truck) / m(truck)
= 15000 kg m/s / 3000 kg
= 5 m/s
Therefore, the velocity of the truck immediately after the collision is 5 m/s.