Two clouds collide and form another, more massive cloud. One cloud is stationary, while the other is traveling at 1 m/s. After the collision, the new, combined cloud travels with a velocity of 0.25 m/s. What is the ratio of the masses of the two original clouds?
To find the ratio of the masses of the two original clouds, 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 denote the mass of the stationary cloud as m1 and the mass of the traveling cloud as m2. We also know the velocities before and after the collision: v1 = 0 m/s (since the stationary cloud has zero velocity) and v2 = 1 m/s.
The momentum equation is given by: m1v1 + m2v2 = (m1 + m2)v, where v is the velocity of the combined cloud after the collision.
Substituting the given values, we get: m1(0) + m2(1) = (m1 + m2)(0.25)
Simplifying further, we have: 0 + m2 = 0.25m1 + 0.25m2
Combining like terms, we get: 0.75m2 = 0.25m1
Dividing both sides by 0.25m2, we have: 3 = m1/m2
Therefore, the ratio of the masses of the two original clouds is 3:1.