Menu div.question,div.steps {font-size: 16px; padding: 10px;line-height: 20px; margin: 20px;} div.question{border: 1px solid #ccc;} div#solution .button{font-size: 20px; margin: 20px; width: 200px; padding: 10px; text-align: center;} div.hint,div.answer,div.steps{display: none;} div.pre_next{font-size: 30px; width:90%; margin:auto;} div.pre_next a.nav_pre{float:left;} div.pre_next a.nav_next{float:right;} div.title div.notes{ font-family:sans-serif, Arial; font-size: 18px; } 5. A package is dropped at time t = 0 from a helicopter that is descending steadily at a speed v_i. (a) What is the speed of the package in terms of v_i, g, and t? (b) What vertical distance d is it from the helicopter in terms of g and t? (c) What are the answers to parts (a) and (b) if the helicopter is rising steadily at the same speed? Hint v_y = v_(yi) + a∆t; y_f = y_i + v_(yi)t + 1/2 a t^2 Answer (a)color(red)(v_y = -v_i - g t) (b)color(red)(d = -1/2 g t^2) (c) part (a) color(red)(v_y = v_i - g t) part (b) color(red)(d = -1/2 g t^2) Show Steps Set upward direction is positive. Known: dropped at time t=0 and a_y = -g Given: v_(yi) = -v_i (a) v_y = v_(yi) + a∆t => color(red)(v_y = -v_i - g t) (b) distance package moved  = y_p distance helicopter moved  = y_h distance between helicopter and package is: d = y_p - y_h y_p = y_i + v_(yi)t + 1/2 a t^2 y_h = y_i + v_(yi)t where y_i = 0 d = -v_i t + 1/2(-g)t^2 - (-v_i t) color(red)(d = -1/2 g t^2) (c) if v_(yi) = +v_i part (a) became color(red)(v_y = v_i - g t) part (b) still color(red)(d = -1/2 g t^2)