A bullet is shot from a spring gun into a sandbox that is suspended from the ceiling as shown in the figure below. The spring constant of the gun is k=1600 N/m and the spring is compressed by x=0.4m before the bullet is fired. The bullet then lodges inside the box. The distance L between the center of mass of the sandbox and the ceiling is 1.0m. The mass m of the bullet is 20 grams while the mass M of the sandbox is 1.0 kg.

a.) What is the initial velocity of the bullet (when it just leaves the gun)?

b.) What is the velocity v of the sandbox just after the bullet is lodged into the box?

c.) What is the impulse J on the bullet imparted by the collision?

d.) If the bullet-sandbox collision lasted for a time interval , t=0.01 sec, what is the average force on the box?

e.) What is the change in kinetic energy of the sandbox bullet system right after the collision?

f.) After the collision process is over, what is the maximum height hmax the sandbox will reach above its initial position?