two equal mass cars collide head to tail and their bumpers lock. One car has a velocity of 10m/s and the other is at rest. what is the velocity of the two cars after the collision?
5, see below
To find the velocity of the two cars 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.
Let's assign some variables:
m1 = mass of the first car
m2 = mass of the second car
v1 = velocity of the first car before the collision (10 m/s in this case)
v2 = velocity of the second car before the collision (0 m/s in this case)
v1' = velocity of the first car after the collision
v2' = velocity of the second car after the collision
Since the initial velocity of the second car is 0, we can write the equation for conservation of momentum as:
(m1 * v1) + (m2 * v2) = (m1 * v1') + (m2 * v2')
Since the cars have equal mass, we can simplify the equation to:
(m1 * v1) = (m1 * v1') + (m2 * v2')
Substituting the given values, we have:
m1 * 10 = m1 * v1' + m2 * v2'
Since the mass of the two cars is equal, we can further simplify the equation to:
10 = v1' + v2'
Since the two cars lock bumper to bumper, their final velocities will be the same (v1' = v2'). Therefore, we can rewrite the equation as:
10 = 2 * v1'
Solving for v1':
v1' = 10 / 2 = 5 m/s
Hence, the velocity of both cars after the collision is 5 m/s.