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 cm, 5 cm, 10 cm,75 cm,76 cm,80 cm
this is a straighforward substitution problem
set you calculator to radians, multiply 2.4 by pi, and press the sine key.
Multiply by 80 and you will get 76.08
well thnks for ur help.
according to that info above i need to choose two correct statements from below.
1) the maximum distance that the machine head moves horizontally from its central starting position is 80 cm.
2) The maximum distance that the machine head moves horizontally from its central starting position is 40 cm.
3) The machine head will make 50 complete cycles in a minute.
4) The machine head will make 30 complete cycles in a minute.
5) The machine head will make one complete cycle in half a minute.
6) The machine head will make one complete cycle in two minutes.
Think about the sine function, its value lies between -1 and 1,
since its maximum value can be 1, and that is multiplied by 80.....
choices 3-6 deal with cycles per minute.
for sin(kx) where k is a constant the period of the curve,(one cycle), is given by 2pi/k
for your equation the period would be 2pi/pi, which is 2
so it takes 2 seconds to complete one cycle.
so...mmhhh? which one would it be???
From the given equation, d = 80 sin (πt), we can see that the amplitude of the oscillation is 80 cm. Therefore, statement 1, "the maximum distance that the machine head moves horizontally from its central starting position is 80 cm," is correct.
To determine the period of the sine wave, we need to find the value that gives us one complete cycle. In this case, one complete cycle occurs when t = 2 seconds (since 2 seconds is the period of the sine function). Therefore, statement 6, "The machine head will make one complete cycle in two minutes," is correct.
As for statements 3, 4, and 5, they all pertain to cycles per minute, which is not consistent with the given time unit of seconds in the equation. Therefore, statements 3, 4, and 5 are incorrect.
In summary, the correct statements are:
1) The maximum distance that the machine head moves horizontally from its central starting position is 80 cm.
6) The machine head will make one complete cycle in two minutes.