a 1500 kg car travelling at 16.7 m/s to the south collides with a 6300 kg truck that is initially at rest at a stop light. the car and the truck sticks togetherand moves together after the collision. what is the final velocity of the two-vehicle mass?
answer in units of m/s..
i solved and got 3.211598462 bt when i entered this answer the answer was wrong... please help..
To solve this problem, we can apply the principles of conservation of momentum.
The momentum before the collision is equal to the momentum after the collision. Momentum is calculated by multiplying mass by velocity.
Let's let the final velocity of the two-vehicle mass be represented by "v."
The momentum of the car before the collision is given by: (mass of the car) * (velocity of the car)
Momentum of the car before collision = (1500 kg) * (-16.7 m/s) = -25,050 kg·m/s
Since the truck is at rest initially, its momentum before the collision is zero.
The momentum of the two-vehicle mass after the collision is given by: (combined mass of the car and truck) * (final velocity of the two-vehicle mass)
Momentum of the two-vehicle mass after collision = (1500 kg + 6300 kg) * v
Now, according to the principle of conservation of momentum, we can set the initial momentum equal to the final momentum:
-25,050 kg·m/s = (1500 kg + 6300 kg) * v
Let's solve for v:
-25,050 kg·m/s = 7800 kg * v
v = -25,050 kg·m/s / 7800 kg
v = -3.215 m/s
The negative sign indicates that the two-vehicle mass is moving in the opposite direction of the initial velocity of the car.
Therefore, the final velocity of the two-vehicle mass is approximately -3.215 m/s.
To solve this problem, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum (p) of an object is calculated by multiplying its mass (m) by its velocity (v):
p = m * v
Before the collision, the momentum of the car is given by:
momentum of car = mass of car * velocity of car
momentum of car = 1500 kg * (-16.7 m/s) (Note: Since the car is moving south, the velocity is negative)
momentum of car = -25050 kg·m/s
The momentum of the truck is initially zero since it is at rest:
momentum of truck = 0 kg·m/s
After the collision, the two vehicles stick together and move as one combined mass. Let's call this combined mass M.
According to the principle of conservation of momentum, the total momentum before and after the collision should be the same:
momentum before collision = momentum after collision
Therefore,
-25050 kg·m/s + 0 kg·m/s = M * final velocity
Now, we need to solve for the final velocity (v):
final velocity = (-25050 kg·m/s) / M
To find M, we can calculate the total mass (m_total) of the two vehicles:
m_total = mass of car + mass of truck
m_total = 1500 kg + 6300 kg
m_total = 7800 kg
Plugging the values back into the equation:
final velocity = (-25050 kg·m/s) / (7800 kg)
final velocity = -3.211 m/s
The negative sign indicates that the two-vehicle mass is moving in the opposite direction, north in this case.
Therefore, the final velocity of the combined mass after the collision is approximately -3.211 m/s.