Question

William Tell shoots an apple from his son's head. The speed of the 102-g arrow just before it strikes the apple is 26.7 m/s, and at the time of impact it is traveling horizontally. If the arrow sticks in the apple and the arrow/apple combination strikes the ground 6.90 m behind the son's feet, how massive was the apple? Assume the son is 1.85 m tall.

Answer 1

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,$m_1V_1+m_2V_2 = (m1+m2)V_f$

To find the speed at which the arrow impacts the apple we turn to the equation of time, in which,

$t= \sqrt{\frac{2h}{g}}$

The linear velocity of an object is given by

$V=\frac{X}{t}$

Replacing the equation of time we have to,

$V_f = \frac{X}{t}\\V_f =\frac{X}{\sqrt{\frac{2h}{g}}}\\V_f = \frac{6.9}{\sqrt{\frac{2(1.85)}{9.8}}}\\V_f = 11.23m/s$

Velocity two is neglected since there is no velocity of said target before the collision, thus,

$m_1V_1 = (m1+m2)V_f$

Clearing for m_2

$m_2 = \frac{m_1V_1}{V_f}-m_1\\m_2 = \frac{(0.102)(26.7)}{11.23}-0.102\\m_2 = 0.1405KG= 140.5g$