A 1600 kg car traveling at 13.7 m/s to the
south collides with a 4600 kg truck that is
initially at rest at a stoplight. The car and
truck stick together and move together after
the collision.
What is the final velocity of the two-vehicle
mass? Assume that North is positive.
Answer in units of m/s
To find the final velocity of the two-vehicle mass, we can use 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.
Before the collision, the car's momentum can be calculated by multiplying its mass (1600 kg) by its velocity (-13.7 m/s) since it is traveling to the south:
Car's initial momentum = mass * velocity = (1600 kg) * (-13.7 m/s) = -21920 kg·m/s
Since the truck is initially at rest, its momentum is zero:
Truck's initial momentum = 0 kg·m/s
After the collision, the car and truck stick together, so their combined mass is the sum of the individual masses:
Combined mass = car's mass + truck's mass = 1600 kg + 4600 kg = 6200 kg
Let's denote the final velocity of the combined mass as V.
Using the principle of conservation of momentum:
Initial total momentum = Final total momentum
(-21920 kg·m/s) + 0 kg·m/s = (combined mass) * (final velocity)
Simplifying the equation:
-21920 kg·m/s = (6200 kg) * V
To find the final velocity, divide both sides of the equation by the combined mass:
V = (-21920 kg·m/s) / (6200 kg)
Calculating the value:
V = -21920 kg·m/s ÷ 6200 kg ≈ -3.54 m/s
Since we assumed that North is positive and the final velocity obtained is negative, we need to consider the magnitude or absolute value of the velocity. Therefore, the final velocity of the two-vehicle mass is approximately 3.54 m/s, with the direction being to the north.
M1*V1 = (M1+M2)*V
M1 = 1600 kg
V1 = 13.7 m/s.
M2 = 4600 kg
Solve for V.