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?

a) h(t)=0.03sin(8πt)+1

b) h(t)=0.03sin(4πt)+1

c) h(t)=0.3sin(8πt)+1

d) h(t) = 0.03 sin (2π/4 t)+1

Julius
Nov 29, 2017

#1**+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 :

https://www.desmos.com/calculator/f9yuhgchgr

CPhill
Nov 29, 2017