Problem $1(10$ points$)$:

impact

The composite rod is made from two segments. Portion $AB$ is steel and $BC$ is aluminum. Determine the maximum height $h$ from which the $W=250N$ collar should be dropped so that the maximum axial stress in the rod does not exceed ${}_{\text{a}\text{l}\text{l}\text{o}\text{w}}.$ A factor of safety of $2$ is used against failure by yielding. $($Given for steel: ${}_Y=250$MPa,$E=200$ GPa ; for aluminum: $($:${}_Y=414$MPa,$E=73$GPa.