Problem $3.(6$ marks$)$ A $200$ ton crawler crane is required to hoist a load of $80,000lb$ from a truck at

ground level and place it on a platform $76ft$ above the ground. The load will be picked up with

slings at the bottom, requiring a minimum vertical distance of $42ft$ from the bottom of the load to

the boom point of the crane. The maximum horizontal distance from the center of rotation of the

crane to the hoist line of the crane when lifting the load is $40ft.$

a$)$ Determine the minimum$-$length boom for the crawler crane.

b$)$ What is the maximum load that can be picked up using the crane if it is already rigged with a

$180\text{'}$ boom.

c$)$ Can the crane make the lift? If not, provide alternatives.