A height above ground, h metres, of a child on a swing, ranges from 0.5m to 1.5m The child reaches max height ever second. Initially there child is at minimum height. Express height as a function of time.
I get h(t)=0.5sin(1t)+1, is this correct?

Question

A height above ground, h metres, of a child on a swing, ranges from 0.5m to 1.5m  The child reaches max height ever second.  Initially there child is at minimum height.  Express height as a function of time.
I get h(t)=0.5sin(1t)+1, is this correct?

ganeshie8 · Answer

Very close! try this :
$$\large   h(t)=0.5\sin(2\pi t)+1$$

ganeshie8 · Answer

that doesn't look correct either.. looks we need to slide the graph to right because the starting value is minimum

ganeshie8 · Answer

` Initially there child is at minimum height.`

ganeshie8 · Answer

try this instead :
$$\large   y=0.5\sin\left(2\pi t-\frac{\pi}{2}\right)+1$$

anonymous · Answer

why 2pi t?

ganeshie8 · Answer

because you want the period to be `1` : 

`The child reaches max height ever second.`

ganeshie8 · Answer

the period of sin(t) is 2pi
since you want to reduce the period to 1,  multiplying t by 2pi compresses the graph by a factor of 2pi

anonymous · Answer

ah ok :)

ganeshie8 · Answer

see the graph https://www.desmos.com/calculator/gxe9rljmmy

anonymous · Answer

Thank you so very very much :)

ganeshie8 · Answer

yw!