Falling Object. The motion of an object moving vertically through the air is governed by the equation where y is the upward vertical displacement and V is a constant called the terminal speed. Take g = 32 ft /sec2 and V = 50 ft/sec. Sketch trajectories in the yv-phase plane for starting from y = 0 and v =-75,-50, -25, 0, 25, 50, and 75 ft/sec. Interpret the trajectories physically; why is V called the terminal speed?

Solution:Step 1:In this problem, we need to find the terminal velocity and we have to sketch trajectories in the yv-phase plane for Step 2:Now we have the motion of an object moving vertically through the air is governed by the equation, where y is the upward vertical displacement and V is a constant called the terminal speed. Take the and V = 50 ft/sec.Now the equation is ………..(1)Let v = Therefore Since Then we get ………(2)Since From equation (2)is the terminal velocity.