- The momentum of an object with mass of m and moving at a velocity of v can be calculated using the formula below.
P=m*vP=m⋅v
- Firstly the equation above must be written for two situation.
color(red)(P=m*v" 'initial case'")P=m⋅v 'initial case'
"P:initial momentum , m:initial mass , v:initial velocity"P:initial momentum , m:initial mass , v:initial velocity
color(green)(P/2=2m*x" 'final case '")P2=2m⋅x 'final case '
P/2:"final momentum , 2m:final mass , x:final velocity"P2:final momentum , 2m:final mass , x:final velocity
- Let's find the ratio of the two equations.
P/(P/2)=(m*v)/(2m*x)PP2=m⋅v2m⋅x
cancel(P)*2/cancel(P)=cancel(m)*v*1/(2 .cancel(m.) x)
2=v/(2x)
2*2x=v
4x=v
x=v/4