The position of the particle is represented by `y=ut-(1)/(2)"gt"^(2)`.
a) What is the force acting on the particle?
b) What is the momentum of the particle?

Explanation

To find the force, we need to find the acceleration experienced by the particle.
The acceleration is given by `a=(d^(2)y)/(dt^(2))`
(or) `a=(dv)/(dt)`
Here
v =velocity of the particle in y direction
`v=(dy)/(dt)=u-"gt"`
The momentum of the particle = mv = m (u-gt).
`a=(dv)/(dt)=-g`
The force acting on the object is given by `F ma =-mg`
The negative sign implies that the force is acting on the negative y direction. This is exactly the force that acts on the object in projectile motion.