To develop the problem, we require the values concerning the conservation of momentum, specifically as given for collisions.
By definition the conservation of momentum tells us that,[tex]m_1V_1+m_2V_2 = (m1+m2)V_f[/tex]
To find the speed at which the arrow impacts the apple we turn to the equation of time, in which,
[tex]t= \sqrt{\frac{2h}{g}}[/tex]
The linear velocity of an object is given by
[tex]V=\frac{X}{t}[/tex]
Replacing the equation of time we have to,
[tex]V_f = \frac{X}{t}\\V_f =\frac{X}{\sqrt{\frac{2h}{g}}}\\V_f = \frac{6.9}{\sqrt{\frac{2(1.85)}{9.8}}}\\V_f = 11.23m/s[/tex]
Velocity two is neglected since there is no velocity of said target before the collision, thus,
[tex]m_1V_1 = (m1+m2)V_f[/tex]
Clearing for m_2
[tex]m_2 = \frac{m_1V_1}{V_f}-m_1\\m_2 = \frac{(0.102)(26.7)}{11.23}-0.102\\m_2 = 0.1405KG= 140.5g[/tex]
