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.
a) 1cm
b) 5 cm
c) 10 cm
d) 75 cm
e) 76 cm
f) 80cm
I have spent a lot of time on this and think it is either B or F. Can anyone help
To find the distance of the head of the machine from the starting position after 2.4 seconds, we can substitute the value of t into the equation d = 80 sin(pi*t).
Calculating this for t = 2.4 seconds:
d = 80 sin(pi*2.4)
d ≈ 80 sin(7.548)
Using a calculator, we find that sin(7.548) ≈ 0.993.
Therefore,
d ≈ 80 * 0.993
d ≈ 79.44
Rounding to the nearest cm, the distance is approximately 79 cm.
Given the options, 79 cm is closest to 80 cm (option f). So the correct answer is f) 80 cm.