Final velocity: v= 1.23 m/s angle: θ = 75.3º
To explain:
Initially, we designate the direction in which both fruits are thrown as the x-axis, meaning all initial momenta will only have horizontal components.
In the absence of external forces influencing the collision—due to the extremely brief timeframe of the event—momentum conservation applies.
As momentum is a vector quantity, both components must be maintained, leading us to establish the following equations:
p₁ₓ = p₂ₓ ⇒ -m₁. vi₁ +m₂. vi₂ = m₁. vf₁. cos θ (1)
p₁y = p₂y ⇒ 0 =m₂. vf₂ - m₁. vf₁. sin θ (2)
Substituting in the values for m1, m₂, vi₁, vi₂, and vf₂ allows us to solve for θ, the angle between the apple and the horizontal, through the following steps:
(1) -0.13 Kg. 1.05 m/s + 0.15 Kg. 1.18 m/s = 0.13. vf. cos θ
(2) 0.15 Kg. 1.03 m/s = 0.13 vf. sin θ
Taking the ratio sin θ / cos θ = 3.82 leads to tg θ = 3.82 ⇒ θ = arc tg (3.82) = 75.3º
Substituting this θ value back into (2) gives us:
0.15 kg. 1.03 m/s = 0.13 vf. sin 75.3º = 0.13. vf. 0.967
Solving for vf yields:
vf = 0.15 kg. 1.03 m/s / (0.13. 0.967) = 1.23 m/s