Answer
(a) No
(b) $3.86cm$
Work Step by Step
(a) We know that the given scenario is an example of an inelastic collision. After the collision, the wad of putty sticks to the block. Thus, the momentum is conserved but not the energy of the system.
(b) We can find the required height as follows:
Initial momentum of the system is given as
$P_i=m_1v_{1i}+m_2v_{2i}=0+m_2v_{2i}=m_2v_{2i}$
Final momentum of the system is given as:
$P_f=(m_1+m_2)v_f$
According to law of conservation of energy
$P_i=P_f$
$\implies m_2v_{2i}=(m_2+m_2)v_f$
$\implies v_f=\frac{m_2v_{2i}}{m_1+m_2}$
We plug in the known values to obtain:
$v_f=\frac{(0.072Kg)(5.74m/s)}{0.42kg+0.072Kg}=0.84m/s$
Now $h=\frac{v_f^2}{2g}$
We plug in the known values to obtain:
$h=\frac{(0.84m/s)^2}{2(9.8m/s)}$
$h=3.86cm$
