The head of an industrial machine moves in a straight line horizontally backwards and forwards from a central position. The movement can be modelled using the sine wave d = 80 sin ( pie t), where d is the horizontal distance (in cm) from the central starting position, and t is the time after the machine starts running (in second).
Choose the one option which gives the distance of the head of the machine (rounded to the nearest cm) from the starting position after 2.4 seconds.
1)
To find the distance of the head of the machine from the starting position after 2.4 seconds, we can substitute the given value of the time, t = 2.4 seconds, into the equation d = 80 sin (πt).
Calculating:
d = 80 sin (π * 2.4)
d = 80 sin (3.14 * 2.4)
d = 80 sin (7.536)
d ≈ 80 * 0.9998
d ≈ 79.984
Rounding to the nearest centimeter, the distance of the head of the machine from the starting position after 2.4 seconds is approximately 80 cm.