# Calculate the final velocity of the cart

Three students, each having a mass of 60 kg, climb onto a large flatbed cart that has a mass of 120 kg. Standing at one end and taking turns they run to the opposite end and jump off, one immediately following the other, each with a velocity of 10 m/s with respect to the cart. Calculate the final velocity of the cart and students with resepect to the earth.

I know that we have to use:
m1*v1 + m2*v2 = m1*v1 + m2*v2

the left side is before and the right side is after
m1 = mass of object A
v1 = velocity of object A
m2 = mass of objectB
v2 = velocity of object B

Any help will be appreciated.

wakingrufus
well i asssume the system starts at rest, so the left side of your equation would = 0 and your equation would reduce to:
m1*v1 + m2*v2 = 0

m1 = mass of the cart
v1 = final velocity of the cart
m2 = mass of a child
v2 = final velocity of a child

you need another equation to solve for 2 variables:

V1 - v2 = 10

solve it for v1:
v1 = 10 + v2
and plug it into your first equation:

120*(10+v2) + (60)(v2) = 0
v2 = -20/3
plug into the second equation: v1 = 10/3

this is just the first step. you have to do it three times, one for each child, using the result from previous one as the initial for the second.