If the net force acting on a laboratory cart as is it being pushed down the hallway is zero, then what is the relationship between fa and ff?

Fa = -Ff provided that the angle between Fa and Ff is zero

Explanation:

Since the net force is zero, the sum of adding all external forces onto the cart must be zero.

Assuming there is no other forces acting on the cart and Fa acting in the same plane as Fc (i.e. zero angle between acting forces),

Fa + Ff = 0

Hence

Fa = -Ff

the velocity you are looking for is made up of two parts: horizontally velocity, vh, and its vertical velocity, vv. the actual velocity of the ball will be these two parts added together, and because velocity is a vector then they will need to be added vectorially.  

neglecting air resistance etc etc.,  

the horizontal velocity component will be constant (because there is no accelerating force in the horizontal direction.  

vh = 8 ms-1  

the vertical velocity component has an accelerating force: 'g'.  

using v = u +at where a = g = 9.81 ms-2.  

the vertical component of velocity, vv = 0 + gt = vv =9.81 x 2  

vv = 19.62 ms-1 . the zero appears because the virtical component of velocity at time t=0 is zero. remember, the ball was thrown horizontally.  

how fast it will be moving (it actual path (being a parabola )) will be the vector sum of these two.  

adding vectorally gives: -  

v = sqr root (8^2 + 19.62^2) = sqr root(64+384.9) = 21.18 or 21.2 ms-1

568.98

explanation:

its math