$15\mathrm{.}35$ In case $($a$),$ a $5-$lb ball is released from rest at position $1$ and falls to position $2.$ In case $($b$),$ the ball is released from rest at position $1$ and swings to position $2.$ For each case, use the principle of work and energy to determine the magnitude of the ball$$s velocity at position $2.[$In case $($b$),$ notice that the force exerted on the ball by the string is perpendicular to the ball$$s path.$]$