Question

the relation between the ball’s vertical position (yy) and the time (tt) and perform a parabolic best fit of the form y = A*t^2 + B*t + C. Interpret the meaning of the fit parameters.

Parameter                 Value

A                                 -6.751 E0

B                                 4.739 E0

C                                -8.885 E-1

y= -6.751x² + 4.739x – 0.885

Does the ball moves at a constant acceleration in the vertical direction?

Answer 1

The position as a function of time given as

m

at t = 0, the position y is = C = -0.8885 m, it means origin or reference point is taken 0.885 m above the point of projection.

If we find derivative of y with respect to time, we will get velocity.

.

This is the velocity as a function of time t

at t=0, the value of velocity is given by B = 4.739 m/s.

on further derivative of y with respect to time, gives acceleration :

the acceleration is ay = A = -13.502 m/s/s which is constant.

Therefore, A = represents half of acceleration = .

B = represents initial velocity

C = represents initial position

Therefore, the acceleration in the vertical direction is constant.