At a time t $=0$ a ball $($A$)$ is dropped from the top of a building of height H$.$ At the

same time t $=0,$ a second ball $($B$)$ is thrown straight upward, from the bottom of the

building, with a speed v$0.$ Some time later, the balls collide a height $3$

$5$ H above the ground

with the balls moving in opposite directions. Answer all of the below parts by expressing

your solutions in terms of the symbols H and the acceleration due to gravity g$.$

$($a$)$ At what time do the two balls collide?

$($b$)$ What must have been the initial speed of ball B when it was thrown?

$($c$)$ What is the relative speed of the balls when they collide?