Question

Archerfish are tropical fish that hunt by shooting drops of water from their mouths at insects above the water’s surface to knock them into the water, where the fish can eat them. A 65-g fish at rest just at the surface of the water can expel a 0.30-g drop of water in a short burst of 5.0 ms. High-speed measurements show that the water has a speed of 2.5 m/s just after the archerfish expels it. What is the speed of the archerfish immediately after it expels the drop of water?

(a) 0.0025 m/s
(b) 0.012 m/s
(c) 0.75 m/s
(d) 2.5 m/s.

Answer 1

(b) 0.012 m/s

Step-by-step explanation:

Given that:

mass (m₁) of the drop of water = 0.30 g = 3.0 × 10⁻⁴ kg

mass (M₂) of the fish = 65 g = 65 × 10⁻³ kg

speed (v₁) of the water = 2.5 m/s

speed (v₂) of the archerfish = ??

By conservation of momentum

m₁v₁ - M₂v₂ = 0

m₁v₁ = M₂v₂

v₂ = m₁v₁ / M₂

v₂ = ( 3.0 × 10⁻⁴ × 2.5 ) / 65 × 10⁻³

v₂ = 0.0115 m/s

v₂ ≅ 0.012 m/s

Therefore, the speed of the archerfish immediately after it expels the drop of water 0.012 m/s.