Question

required information
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. the fish is to
successfully spit at and strike the grasshopper, which is 0.200 m
away horizontally and 0.215 m above his mouth.

what angle (in degrees) above the horizontal must he spit? assume ( v_{fy} = 0 ).
\boxed{}°

Explanation:

Step1: Define horizontal/vertical displacements

Let $x = 0.200\ \text{m}$ (horizontal distance), $y = 0.215\ \text{m}$ (vertical height).

Step2: Use projectile velocity relation

For $v_{fy}=0$ (vertical final velocity at target), the relation between angle $\theta$, $x$, and $y$ is derived from projectile kinematics:
$$\tan\theta = \frac{2y}{x}$$

Step3: Calculate tangent of the angle

Substitute values:
$$\tan\theta = \frac{2\times0.215}{0.200} = 2.15$$

Step4: Find angle in degrees

Take arctangent:
$$\theta = \arctan(2.15)$$

Answer:

$65.2^\circ$