Question

A hammer thrower is competing in a track and field meet. He rotates exactly 5 times in 2π seconds, and the motion of his hammer is represented by a sine function.

Which function rule could model this situation?
f(x)=5 sin x
f(x)= sin(5x)
f(x)=5π sin x
f(x)= sin(1/5x)

Answer 1

Therefore the correct option is sin(5x).

Explanation:

i) The hammer thrower rotates exactly 5 times in 2
`\pi` seconds.

Therefore one rotation is completed in
`(2\pi )/(5)` seconds.

ii) Since the motion of the hammer is represented by a sine function therefore

one rotation is considered to be one full cycle and the time period of that cycle

is given in equation i) and it is T =
`(2\pi )/(5)` seconds.

iii) the equation of a sine function is given by sin(2
`\pi`
`(1)/(T)`) which in this case would

be sin(2
`\pi` ×
`(1)/((2\pi )/(5))` × x) = sin(5x)

iv) Therefore the answer is sin(5x)