Final answer:
To determine an object's final velocity squared (v'^2) in vertical motion, we use the equation v^2 = vy^2 - 2g(y - yo). In two-dimensional motion, we separate into horizontal and vertical components, where the horizontal displacement may involve x = xo + vt, and finally, we recombine the two using vector addition techniques.
Step-by-step explanation:
To solve for an object's final velocity squared (v'^2) after a certain displacement on the y-axis, we use the kinematic equation v^2 = v_y^2 - 2g(y - y_o), where g is the acceleration due to gravity, y is the final vertical position, and y_o is the initial vertical position. This equation simplifies calculations in the vertical direction because it does not involve time (t), which might not be known.
Additionally, in problems involving two-dimensional motion, we often separate the motion into horizontal and vertical components. For horizontal motion, we might use an equation like x = x_o + vt, if acceleration is zero. To solve for displacement (x), we identify the initial position (x_o), the constant velocity (v), and the time (t).
Finally, to find the total displacement and velocity, we would recombine the horizontal and vertical components. For displacement, we employ the Pythagorean theorem (A = √A^2 + A^2), and for velocity, we calculate the direction using the inverse tangent function (θ = tan^-1(Ay/Ax)).