Two objects collide in an elastic collision. If object 1 is traveling with a velocity of 7.5 m/s and object 2 is traveling with a velocity of – 2.5 m/s. what is the final velocity of each object?

Question

The mass of object 1 is 3.0 kg, three times the mass of object 2

619 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-07T09:45:29

The velocity of the first object is #=2.5ms^-1#
The velocity of the second object is #=12.5ms^-1#

In an elastic collision, we have conservation of momentum and conservation of kinetic energy,

#m_1u_1+m_2u_2=m_1v_1+m_2v_2#

and

#1/2m_1u_1^2+1/2m_2u_2^2=1/2m_1v_1^2+1/2m_2v_2^2#

Solving the above 2 equations for #v_1# and #v_2#, we get

#v_1=(m_1-m_2)/(m_1+m_2)*u_1+(2m_2)/(m_1+m_2)*u_2#

and

#v_2=(2m_1)/(m_1+m_2)*u_1+(m_2-m_1)/(m_1+m_2)*u_2#

#m_1=3kg#

#m_2=1kg#

#u_1=7.5ms^-1#

#u_2=-2.5ms^-1#

Therefore,

#v_1=2/4*7.5+2/4*(-2.5)=5/2=2.5ms^-1#

#v_2=6/4*7.5-2/4*(-2.5)=12.5ms^-1#

Verificaition

#m_1u_1+m_2u_2=3*7.5-1*2.5=20#

#m_1v_1+m_2v_2=3*2.5+12.5=20#