The 40-kg package is thrown with a speed of 4 m/s onto the cart having a mass of 20 kg....

From conservation of momentum, we have for the horizontal direction

By substituting values of paramteres into the above relation, we have

From conservation of momentum, we have when the spring is fully compressed

By substituting values of paramteres into the above relation, we have

Velocity of the cart is

Let the stiffness of the spring be

Initial elastic potential energy in each spring is expressed as

Accordignly, we have

Final elastic potential energy in each spring is expressed as

Accordignly, we have

From the conservation of energy principle, we have

Accordignly, we have

Maximum compression of the spring is