Question

A ball is thrown vertically upward with a velocity of 15 m/s from the roof of building that is 22 m high. How long does it take to hit the ground below? How fast was it going when it hit?

Answer 1

$\\ALONG\;VERTICAL\;\\\\ initial\;velocity\;v_{oy}=15\;m/s\\\\ acceleration\;a_y=-g=-9.8\;m/s^2\\\\ initial\;position\;y_o=22\\\\ (i)\\\\ final\;position\;y=0\\\\ from\;equation\;of\;motion\\\\ y-y_{o}=v_{oy}t&plus;\frac{1}{2}a_{y}t^2\\\\ 0-22=(15)(t)-\frac{1}{2}(9.8)(t^2)\\\\ t=4.14\;s\;<<<------answer\\\\ (ii)\\\\ from\;equation\;of\;motion\\\\ v_y^2-v_o^2=2\;a_y\;(y-y_{o})\\\\ v_y^2-15^2=(2)(-9.8)(0-22)\\\\ v_y^2-15^2=2\times 9.8\times 22\\\\ v_y=25.6\;m/s<<<------answer\\\\$