Question

A ball is thrown horizontally from the roof of a building 60 ft high at 80 ft/s. What will be the ball's velocity when it strikes the ground?

Answer 1

Conservation of energy gives the vertical final velocity \(v_{y_f}\).\[\underbrace{mgh}_{\text{PE}}=\underbrace{\frac{1}{2}mv_{y,f}^2}_{\text{KE}} \Rightarrow v_{y,f}=\sqrt{2gh}\]The horizontal velocity \(v_x\) is invariant with respect to time since it is perpendicular to gravitational forces. The final velocity is given by the Pythagorean Theorem.\[v_f = \sqrt{v_x^2+v_{y,f}^2} \Rightarrow \boxed{v_f = \sqrt{v_x^2 + 2gh}}\]