As discussed in Example 4-7, the archcrfish 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 2.15 m/s at an angle of 52.0° above the horizontal, and aims for a beetle on a leaf 3.00 cm above the water's surface, (a) At what horizontal distance from the beetle should the archerfish fire if it is to hit its target in the least time? (b) How much time will the beetle have to react?

Solution 81GP

Step 1 of 3:

Calculate the horizontal distance between the beetle and arch fish for minimum time to strike. Then calculate the time beetle have to react.

(a)

Step 2 of 3:

Given data:

Height

Initial speed

Launching angle

Consider is the time taken to reach the height.

The vertical component of the velocity is

The height reached at time is given by

Hence, we have,

and

So the minimum time is , and the horizontal component of the velocity is

Hence, horizontal distance is

Hence, the horizontal distance between the arch fish and the beetle will be 2.10 cm for minimum time.

(b)