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 18 cm above the waterline and a horizontal distance of 28 cm away. The fish aims its stream at an angle of 39° from the waterline.

Required:
Determine the height above the waterline that the stream reaches at the horizontal position of the insect.

Answer 1

The fish gobbles the mosquito at height 18 cm.

Step-by-step explanation:

Initial velocity, u = 3.7 m/s

horizontal distance, d = 28 cm

Angle, A = 39 degree

Let the time is t.

Horizontal distance = horizontal velocity x time

d = u cos A x t

0.28 = 3.7 cos 39 x t

t = 0.097 s

Let the height is h.

Use the second equation of motion

`h =u t-0.5 gt^2\\\\h= u sin A t - 0.5 gt^2\\\\h= 3.7 sin 39 * 0.097 - 0.5* 9.8* 0.097*0.097\\\\h =0.226 -0.046 \\\\h=0.18 m=18 cm`