Question

A 66.0-kg boy and his 45.0-kg sister, both wearing roller blades, face each other at rest. The girl pushes the boy hard, sending him backward with a velocity 2.80 m/s toward the west. Ignore friction. (a) Describe the subsequent motion of the girl.

Answer 1

the girl moves towards right with a velocity of 4.1m/s

Step-by-step explanation:

Since the system is isolated the momentum of the system is conserved

Initial momentum = Final Momentum

Since initially the system is at rest thus
`\overrightarrow{p_(i)}=0`

Now the final momentum of boy =
`m_(boy)×velocity`

`\overrightarrow{p_(boy)}=66.0* -2.80m/s\\\\\overrightarrow{p_(boy)}=-184.8kgm/s`

Now for girl let the velocity = u hence her moumentum is 45
`* u`

Thus equating final momentum to zero we have

`-184.8kgm/s`+
`45* u = 0`

`u=(184.8)/(45)m/s`

hence
`u=4.1m/s`

Thus the girl moves towards right with a velocity of 4.1m/s