Question

The archerfish hunts by dislodging an unsuspecting insect from its resting place with a stream of water expelled from the fish's mouth. Suppose the archerfish squirts water with a speed of 2.35 m/s at an angle of 56.0 ∘ above the horizontal, and aims for a beetle on a leaf 3.00 cm above the water's surface.

Answer 1

vo = 2.35 m/s
theta = 56.0 deg
y = 3.00 cm = 0.03 m
x = ?

y = vo sin(theta) t - 1/2 * gt^2
0.03 = 2.35 sin(56.0 deg) t - 1/2 * 9.8 * t^2
0.03 = 1.948 t - 4.9 t^2
4.9 t^2 - 1.948 t + 0.03 = 0
t = 0.0160 s, 0.3815 s
Maximum value of t = 0.3815 s
Maximum value of x = vo cos(theta) * t
= 2.35 cos(56.0 deg) * 0.3815
= 0.5013 m = 50.13 cm

The beatle has 0.3815 s to react.
Ans: 50.13 cm, 0.3815 s