Meriam, Kraige & Bolton — Kinematics of Particles: Problem 2_209

*2/209 A baseball is dropped from an altitude \( h = 200 \text{ ft} \) and is found to be traveling at \( 85 \text{ ft/sec} \) when it strikes the ground. In addition to gravitational acceleration, which may be assumed constant, air resistance causes a deceleration component of magnitude \( kv^2 \), where \( v \) is the speed and \( k \) is a constant. Determine the value of the coefficient \( k \). Plot the speed of the baseball as a function of altitude \( y \). If the baseball were dropped from a high altitude, but one at which \( g \) may still be assumed constant, what would be the terminal velocity \( v_t \)? (The terminal velocity is that speed at which the acceleration of gravity and that due to air resistance are equal and opposite, so that the baseball drops at a constant speed.) If the baseball were dropped from \( h = 200 \text{ ft} \), at what speed \( v' \) would it strike the ground if air resistance were neglected?