Answer
See the detailed answer below.
Work Step by Step
a) A clay ball of mass 0.1 kg is moving horizontally at a speed of 3 m/s when it hits a 0.2 kg block that is on a frictionless surface and sticks with it. The two objects now are moving as one unit at a speed of $v_{1x}$ when they hit a spring that has a constant of 3.0 N/m and compressed it a distance of $\Delta x_2$ when the whole system stopped. Find $v_{1x}$ and $\Delta x_2$.
b) See the figures below.
c)
From the first given formula,
$$v_{1x}=\dfrac{0.1\times 3}{0.1+0.3}=\color{red}{\bf 1.0}\;\rm m/s$$
From the second given formula,
$$\Delta x_2 =\sqrt{\dfrac{0.3v_{1x}^2}{3}}=\sqrt{\dfrac{0.3}{3}}v_{1x}=\sqrt{\dfrac{0.3}{3}}v_{1x}\times 1$$
$$\Delta x_2 =\color{red}{\bf0.32}\;\rm m$$
