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

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

Step-by-step 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=(v_(0)^(2)sin^(2) \Theta)/(2g)`, as we clear it for
`v_(0)`, we obtain,
`v_(0)=(√(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.