Question

An archer fish spies a meal of a grasshopper sitting on a long stalk of grass at the edge of the pond in which he is swimming. If the fish is to successfully spit at and strike the grasshopper, which is 0.200 m away horizontally and 0.525 m above his mouth, what is the minimum speed at which the archer fish must spit?

Answer 1

Answer:

The archerfish must spit at a minimum speed of $3.43m/s$ at an angle of $69.14\°$ above the horizontal.

Explanation:

Hi

First of all, we need to find the angle above the horizontal at which the archerfish must spit, as we can see in the attachment this angle is $\Theta = 69.14\°$.

Then we use the formula $h=\frac{v_{0}^{2}sin^{2} \Theta}{2g}$, as we clear it for $v_{0}$, we obtain, $v_{0}=\frac{\sqrt{2gh} }{sin\Theta}=\frac{\sqrt{2(9.8m/s^{2})(0.525m)} }{sin(69.14\°)}=3.43m/s$, therefore the archerfish must spit at a minimum speed of $3.43m/s$ at an angle of $69.14\°$ above the horizontal.