You do 120 j of work while pulling your sister back on a swing, whose chain is 5.10 m long. you start with the swing hanging vertically and pull it until the chain makes an angle of 32.0â° with the vertical with your sister is at rest. what is your sister's mass, assuming negligible friction?

The work done to pull the sister back on the swing is equal to the increase in potential energy of the sister:
(1)

where m is the sister's mass, g is the gravitational acceleration and  is the increase in altitude of the sister with respect to its initial position.

By calling  the angle of the chain with respect to the vertical, the increase in altitude is given by
(2)
where L is the length of the chain.

Putting (2) inside (1), we find

from which we can find the mass of the sister:

Since you have not included the experiment situation and the data, of course, i can not give you specific details about it. but i can you with this question.1) i will assume that the motion is projectile (parabolic) motion.2) yes, the horizontal distance depends on the horizontal velocity as, naming vx the horizontal velocity and t the time, it is: x = vx × t3) now, observe that the flight time depends on the vertical velocity as, naming voy the initial vertical velocity, t the time and y the vertical distance before reaching the ground: y = yo + voy×t - gt² / 2.the higher the initial vertical velocity (voy) the longer the object will be flying and so t will be higher in the equation for the horizontal distance.that explains the relationship between the horizontal distance and the horizontal velocity.