To solve the problem it is necessary to apply the concepts related to Kepler's third law as well as the calculation of distances in orbits with eccentricities.
Kepler's third law tells us that

Where
T= Period
G= Gravitational constant
M = Mass of the sun
a= The semimajor axis of the comet's orbit
The period in years would be given by

PART A) Replacing the values to find a, we have




Therefore the semimajor axis is 
PART B) If the semi-major axis a and the eccentricity e of an orbit are known, then the periapsis and apoapsis distances can be calculated by



Explanation:
"1 meter per second per second" means acceleration of an object. It is equal to the rate of change of velocity. Its SI unit is
.
It is simply given by :

dv is change in velocity
dt is small interval of time
"1 meter per second per second" means that the velocity of an object can increase by 1 meter per second.
Answer: the child's centripetal acceleration=24.50 m/s²
Explanation:
Given that mass of child= 50 kg
radius of merry go round= 2.25m
angular speed = 3.30 rad/s
Centripetal Acceleration = v²/ r
But V= ωr
So Centripetal Acceleration = v²/ r = (ωr)²/ r
=(3.30)² x (2.25)²/ 2.25 = (3.30)² x 2.25
=24.5025m/s²
=24.50 m/s²