Question

Ex:2
A 2kg, toy truck moving at 4m/s is about to
collide with a lkg toy car moving at 17m/s
in the opposite direction find their combined
velocity after collision, if they stick to each other
(Neglect friction)
Pi = pf​

Answer 1

Answer:

3m/s

Explanation:

by momentum conservation

pi=pf;  initial momentum: (17 x 1) - (2 x 4)=9kgm/s

          final momentum: after collision mass becomes 3kg(since they stick to each other)

                                       therefore;9=3 x v

                                                      v=3m/s

Answer 2

Given:

Mass of toy truck, m₁= 2 kg

Initial velocity of toy truck,u₁= 4 m/s

Mass of toy car, m₂= 1 kg

Initial velocity of toy truck,u₂= -17 m/s

To Find:

Combined velocity of both toys after collision

Solution:

We know that,

• If two bodies moving in same line towards each other collide, then combined velocity or common velocity V is given by

$\pink{\boxed{\bf{V=\dfrac{m_{1}u_{1}+m_{2}u_{2}}{m_{1}+m_{2}}}}}$

where,

m₁ is mass of first body

v₁ is initial velocity of first body

m₂ is mass of second body

v₂ is initial velocity of second body

$\rule{190}{1}$

Note: Here direction of velocity of truck is taken positive and direction of velocity of car is taken negative.

Let the combined velocity of both the toys be V

So,

$\longrightarrow\rm{V=\dfrac{m_{1}u_{1}+m_{2}u_{2}}{m_{1}+m_{2}}}}}$

$\longrightarrow\rm{V=\dfrac{2\times4+1\times(-17)}{2+1}}}}$

$\longrightarrow\rm{V=\dfrac{8-17}{3}}}}$

$\longrightarrow\rm{V=\dfrac{-9}{3}}}}$

$\longrightarrow\rm\green{V=-3\ m/s}}}$

Here, negative sign shows that direction of combined velocity is same as the direction of velocity of toy car

So, the magnitude of combined velocity is 3 m/s.