Question

A boy of mass 50kg running 5m/s jumps on to a 20 kg trolley traveling in the same direction at 1.5m/s find their common velocity?

Answer 1

According to the law of conservation of momentum,

m1u1+ m2u2 = m1v1+ m2v2

but, in this case the right hand side of the equation would not be the same as both the masses combine and then have a common velocity. So, the equation goes as follows:

m1u1+ m2u2 = (m1 + m2)v

Let's substitute the values, and we get

m1= 50 kg

m2= 20 kg

u1 = 5m/s

u2= 1.5 m/s

so now we get:

50*5+ 20*1.5= (50+20)v

250+ 30= 70v

280 =70 v

v= 4m/s

Their common velocity is 4m/s.

Answer 2

Mass of boy = m1 = 50 kg

Mass of trolley = m2 = 20 kg

Initial velocity of boy = u1 = 5 ms-1

Initial velocity of trolley = u2 = 1.5 ms-1

Final velocity =

v = m1u1 + m2u2 \ m1 + m2

50 × 5 + 20 × 1.5 ÷ 50 + 20

= 4ms-1

HOPE IT HELPS YOU!!!