A projectile is ejected into an experimental fluid at time $t = 0$. The initial speed is $v_0 = 17.1 \, m/s$ and the angle to the horizontal is $\theta = 40^\circ$.
The drag on the projectile results in an acceleration term $a_D = -kv$ where $k = 0.19 \, s^{-1}$ and $v$ is the velocity of the projectile. Determine the x- and y-components of both the velocity and displacement at time $t = 1.8 \, s$. What is the terminal velocity? Include the effects of gravitational acceleration and assume that the projectile enters a deep portion of the pool, and never reaches the surface of the fluid.
Answers:
Displacement at time $t = 1.8 \, s$, $x = \text{_____} \, m$, $y = \text{_____} \, m$
Velocity at time $t = 1.8 \, s$, $v_x = \text{_____} \, m/s$, $v_y = \text{_____} \, m/s$
The terminal velocity, $v_x = \text{_____} \, m/s$, $v_y = \text{_____} \, m/s$