Question

A boy of mass 60kg running at 3m/s jumps jumps on to a trolly of mass 140kg moving with a velocity of 1.5m/s in the same direction . find their common velocity .

Answer 1

this question is based on conservation of momentum...
initial momentum= final momentum..
common velocity means both trolley and boy moves with same velocity..
now..
initial momentum=60×3+140×1.5
=180 + 210
=390 kgm/s
final momentum=(60+140)V
200V
so on equating..
200V=390
V=390/200=1.95m/s ..ans..

Answer 2

Given :

Mass of boy (m₁) = 60 Kg

Initial velocity of boy (v₁) = 3 m/sec

Mass of trolly (m₂) = 140 Kg

Initial velocity of trolly (v₂) = 1.5 m/sec

To Find :

Common velocity of trolly and boy

Solution :

Let the common velocity of boy and trolly be 'V'

Using Conservation of Linear momentum principle, we have

     m₁v₁  +  m₂v₂     =   (m₁  +  m₂)V

⇒  60×3 + 140×1.5  =   (60 + 140)V

⇒  180  +  210         =    200V

⇒      390                =    200V

⇒       V                   =    $\frac{390}{200}$

∴        V                   =   1.95 m/sec

Therefore, the common velocity of boy and the trolly is 1.95 m/sec.