Question

You and a friend each hold a lump of wet clay. Each lump has a mass of 30 grams. You each toss your lump of clay into the air, where the lumps collide and stick together. Just before the impact, the velocity of one lump was < 3, 3, -3 > m/s, and the velocity of the other lump was < -4, 0, -4 > m/s. What is the velocity of the stuck-together lump just after the collision

Answer 1

`<-0.5, 1.5, -3.5>\ \text{m/s}`

Step-by-step explanation:

`u_1` = Velocity of one lump =
`3x+3y-3z`

`u_2` = Velocity of the other lump =
`-4x+0y-4z`

m = Mass of each lump =
`30\ \text{g}`

The collision is perfectly inelastic as the lumps stick to each other so we have the relation

`mu_1+mu_2=(m+m)v\\\Rightarrow m(u_1+u_2)=2mv\\\Rightarrow v=(u_1+u_2)/(2)\\\Rightarrow v=(3x+3y-3z-4x+0y-4z)/(2)\\\Rightarrow v=-0.5x+1.5y-3.5z=<-0.5, 1.5, -3.5>\ \text{m/s}`

The velocity of the stuck-together lump just after the collision is
`<-0.5, 1.5, -3.5>\ \text{m/s}`.