Abowling ball with a mass of 4.5 kg travels at a velocity of 37 m/s for 2.5 s until it is stopped at the end of the lane by the ball return. what additional information is required to determine the weight of the bowling ball?
a. the speed at which the ball return captured the ball
b. the amount of friction from the bowling lane acting on the bowling ball
c. the acceleration due to gravity acting on the bowling ball
d. the force the bowler applied to the bowling ball

No additional information is required.  We can calculate,
or simply write down, each of those answers now.

A).  The weight of the ball:

    Weight = (mass) x (gravity) = (4.5 kg) x (9.8 m/s²) = 44.1 newtons

B).  Friction acting on the ball:

       You said that the ball travels with speed of 37 m/s for
       2.5 seconds.  Since the speed of the ball is constant,
       there can't be any friction acting on it.  If there were any,
       then it would lose kinetic energy, and its speed would be
       decreasing.

C).  The acceleration due to gravity is 9.8 m/s² ... IF this story is
        taking place on Earth.

D).  Welll, you caught me.  I can't answer this one without
more information.

The bowler applied force to the ball, and accelerated it from
no speed up to 37 m/s.  In order to figure out the acceleration,
I would need to know how long he spent doing it. 

But wait !  You know what ?  Now that I think of it, we would need
a WHOLE LOT of additional information to answer this part, and
we probably still could not answer it. 

The ball didn't get its entire speed of 37 m/s from the bowler pushing
on it.  We don't put bowling balls down on the floor and accelerate
them with constant force.  We swing them up behind us, and let
gravity accelerate them as they swing down like a pendulum. 
So a lot of the force that accelerates the ball comes from gravity,
the rest comes from the bowler, and the amount is different for
every bowler.

So I'm going to say that d). can't be answered at all, period.

And by the way ... one more comment:

37 m/s is just about 83 miles per hour !  I'm not sure the ball return
is going to stop that thing, and I'd want to get out of the way if I were
you or one of the pins !