Question

The archerfish uses a remarkable method for catching insects sitting on branches or leaves above the waterline. The fish rises to the surface and then shoots out a stream of water precisely aimed to knock the insect off its perch into the water, where the archerfish gobbles it up. Scientists have measured the speed of the water stream exiting the fish's mouth to be 3.7 m/s. An archerfish spots an insect sitting 21 cm above the waterline and a horizontal distance of 31 cm away. The fish aims its stream at an angle of 41 ∘ from the waterline. Determine the height above the waterline that the stream reaches at the horizontal position of the insect. DO NOT USE THE KINEMATIC EQUATIONS.

Answer 1

The given problem is a case horizontal projectile motion.

The equation of trajectory for projectile motion, is given by

                                            

Where, u is initial velocity of the projectile,

             (x , y) is the coordinate of the projectile in the cartesian coordinate system

             is the angle at which projectile wass launched and

             g = 9.8 m/s² is acceleration due to gravity

Here, the water stream is our projectile. u = 3.7 m/s , x = 31 cm = 0.31 m, and .

Putting these values in the equation of trajectory, we get

                                            

                                                

Hence, the strem will reach a height of 21 cm above the waterline at the horizontal position of the insect. i.e. the strem will hit the insect.

For any doubt please comment.