Question

A trolley is moving with a velocity of 20 meter per second. The mass of the trolley 100.8 kg and Apple mass of 0.2 kg is moving with a velocity of 5 km/s. The apple falls on the trolley. What is the final velocity of apple trolley together?

Answer 1

Refer to the diagram above.
Linear momentum will remain conserved along horizontal
so $P_i=100.8\ast 20kgm/s$
$P_f=(100.8+0.2)vkgm/s$
By conservation of momentum,
$P_i=P_f$
$2016=101v$
$v=2016/101=19.96m/s$.
If apple velocity is horizontal then result will be different.
In that case,

$P_i=100.8\ast 20+0.2\ast 5000=3016kg-m/s$
and $P_f=101v$
and $v=3016/101=29.8m/s$.