Meriam, Kraige & Bolton — Kinematics of Particles: Problem 2_33

2/33 A projectile is fired downward with initial speed \(v_0\) in an experimental fluid and experiences an acceleration \(a = \sigma - \eta v^2\), where \(\sigma\) and \(\eta\) are positive constants and \(v\) is the projectile speed. Determine the distance traveled by the projectile when its speed has been reduced to one-half of the initial speed \(v_0\). Also, determine the terminal velocity of the projectile. Evaluate for \(\sigma = 0.7 \text{ m/s}^2\), \(\eta = 0.2 \text{ m}^{-1}\), and \(v_0 = 4 \text{ m/s}\).