A ball moves along a 1D coordinate system with the following motion parameters at time t = 0 s: x0 = 6.2 m and v0 = 0 m/s. The ball has a constant acceleration of 2.8 m/s2 during the entire motion which occurs over a time of 1.7 s. Assume that an error in position of 3 % is acceptable in this application over the entire motion. How many rows N will be needed in the table to model the entire motion to within the required error even though you are leaving out the final term of 1/2 a (\Delta t\: Δ t )2 ) present in the exact position expression?
Xo = initial position = 6.2 m
vo = initial velocity = 0 m/s
a = acceleration = 2.8 m/s2
X = final position
t = time interval = 1.7 sec
using the equation
X = Xo + vo t + (0.5) a t2
X = 6.2 + 0 t + (0.5) (2.8) (1.7)2
X = 4.05 m
X' = position with error
Given that :
(X' - X)/X = 0.03
(X' - 4.05)/4.05 = 0.03
X' = 4.17 m
n = number of rows
number of rows are given as
n = 2 X/X'
n = 2 x 4.05 /4.17
n = 2
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