The crank on a pencil sharpener's max height reaches to 3 cm above its centre axis which is 1 m off the ground and can be spun 4 times in a second. Which function models the crank height, h(t), where t is in seconds?
d) h(t) = 0.03 sin (2π/4 t)+1
There are 4 periods in each second
So....eaach period lasts 1/4 seconds
At t = 0, let the height = 1 m
So...at 1/16 seconds the max ht is reached
At 2/16 seconds the height returns to 1m
At 3/16 seconds, the min height is reached = 1m - .03m = .97m
And at 4/16 = 1/4 second it returns to a height of 1m
Note that the sin is maxed at pi/2
So....at 1/16 seconds....we have that .03 sin (8pi *1 /16) + 1 = .03sin (8pi/16) + 1 =
.03sin (pi/2) + 1 = .03(1) + 1 = .03 + 1 = 1.03m
So.....the function is
h(t) = sin ( 8pi * t) + 1 = choice " a "
See the graph here :