Object 1 is moving along the x axis with an initial momentum +16 kg·m/s, where t

Question

Object 1 is moving along the x axis with an initial momentum +16 kg·m/s, where the + sign indicates that it is moving to the right. As the drawing shows, object 1 collides with a second object that is initially at rest. The collision is not head-on, so the objects move off in different directions after the collision. The net external force acting on the two-object system is zero. After the collision, object 1 has a momentum whose x component is +6 kg·m/s. What is the x-component of the momentum of object 2 after the collision?

A detailed explanation on how to solve this would be greatly appreciated.

Explanation / Answer

let m1 be the mass moving with initial velocity u m/s

let m2 be the mass initially at rest.

so the initial momentum along x dirextion = m1u + 0 = 16kg m/s

Let the final velocity of m1 after collosion = V1 m/s

Let the final velocity of m2 after collosion = V2 m/s

During an elastic collosion between two masses , (one at rest and second one moving), they both shoot off in different directions such that angle between them is 90.)

So if the mass m1 makes an angle with x axis then m2 will make an angle (90-) with x axis,

The x component of final velcity of m1= V1Cos

x component of Momentum of m1 after collosion= m1V1cos = 6 kg m/s

X component of final velocity of m2 = V2Cos(90-)= V2Sin

x componnet of momentum of m2= m2v2Sin

m1u1 = m1V1cos + m2v2Sin

16 = 6 + m2v2Sin

m2v2Sin= 10 kg m/s --------------x component of M2  after collosion

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