Respuesta :
Answer:
M = 0.31 kg
Explanation:
This exercise must be done in parts, let's start by finding the speed of the set arrow plus apple, for this we define a system formed by the arrow and the apple, therefore the forces during the collision are internal and the moment is conserved
let's use m for the mass of the arrow with velocity v₁ = 20.4 m / s and M for the mass of the apple
initial instant. Just before the crash
p₀ = m v₁ + M 0
instant fianl. Right after the crash
p_f = (m + M) v
p₀ = p_f
m v₁ = (m + M) v
v =[tex]\frac{m}{m+M} \ v_1[/tex] (1)
now we can work the arrow plus apple set when it leaves the child's head with horizontal speed and reaches the floor at x = 8 m. We can use kinematics to find the velocity of the set
x = v t
y = y₀ + [tex]v_{oy}[/tex] t - ½ g t²
when it reaches the ground, its height is y = 0 and as it comes out horizontally, [tex]v_{oy} = 0[/tex]
0 = h - ½ g t²
t² = 2h / g
For the solution of the exercise, the height of the child must be known, suppose that h = 1 m
t = [tex]\sqrt{ \frac{ 2 \ 1}{9.8} }[/tex]
t = 0.452 s
let's find the initial velocity
v = v / t
v = 8 / 0.452
v = 17.7 m / s
From equation 1
v = m / (m + M) v₁
m + M = [tex]m \ \frac{v_1}{v}[/tex]
M = m + m \ \frac{v_1}{v}
we calculate
M = 0.144 + 0.144 [tex]\frac{20.4}{17.7}[/tex]
M = 0.31 kg
