Question:

A tank car is stopped by two spring bumpers A and B, having stiffness ${ k }_{ A }$ and ${ k }_{ B }$ respectively. Bumper A is attached to the car, whereas bumper B is attached to the wall. If the car has a weight W and is freely coasting at speed ${ v }_{ c }$ determine the maximum deflection of each spring at the instant the bumpers stop the car.Given: ${ k }_{ A }$ = 15 × ${ 10 }^{ 3 }$ lb/ft , ${ k }_{ B }$ = 20 × ${ 10 }^{ 3 }$ lb/ft , W = 25 × ${ 10 }^{ 3 }$ lb , ${ v }_{ c }$= 3 ft/s