# Math Help - Sinusoidal function question.

1. ## Sinusoidal function question.

The diameter of a car's tire is 52cm. while the car is being driven, the tire picks up a nail.
a) how high above the ground will the nail be after the car has travelled 0.1 km?
b) how far will the car have travelled when the nail reaches a height of 20 cm above the ground for the fifth time?

can you explain how to solve this question using an equation and without using an equation?

2. Originally Posted by DeeptiS
The diameter of a car's tire is 52cm. while the car is being driven, the tire picks up a nail.
a) how high above the ground will the nail be after the car has travelled 0.1 km?
b) how far will the car have travelled when the nail reaches a height of 20 cm above the ground for the fifth time?

can you explain how to solve this question using an equation and without using an equation?
$\displaystyle \theta = \frac{x}{r} = \frac{x}{0.26}$

height, $y$ , above the ground in meters is a function of distance, $x$ , the tire has rolled in meters ...

$\displaystyle y = 0.26\left[1-\cos\left(\frac{x}{0.26}\right)\right]$

note the graph of height vs. distance rolled ...

3. can you please explain how you came up with the equation?

4. Originally Posted by DeeptiS
can you please explain how you came up with the equation?
started by sketching the sinusoidal graph of the nail's vertical position as the tire rolls ... saw that it was an inverted cosine curve ... fitted the given parameters.