# Trig. Ratio Word Problem

• Aug 18th 2008, 12:18 PM
topaz192
Trig. Ratio Word Problem
I have no idea how to follow through and do this!

When rounding a curve, the acute angle [ 0 wit ~ through it lol ] that a runners body makes with the vertical is called the angle of incline. It is described by the equation: tan [ 0 wit ~ through it ] = V squared / gr, where v is the velocity of the runner, and g is the acceleration due to gravity. and r is the radius of the track. Acceleration due to gravity is a constant 9.8 meters per second squared. Suppose the radius of the track is 15.5 meters.

a. what is the runners velocity if the angle of incline is 11 degrees? 13 degrees? 15 degrees? should the runner increase/decrease her velocity to increase his or her angle of incline?

i have no idea what to do. do i use the formula at the top?
• Aug 18th 2008, 01:04 PM
thelostchild
hey topaz
yes you should use the formula given with a little rearrangement
remember $\displaystyle \theta$ denotes an angle

we want to solve $\displaystyle \tan \theta = \frac{v^2}{gr}$ for v

so $\displaystyle v=\sqrt {gr \tan \theta}$

now to find the velocity we just plug in the numbers given so for 11º
$\displaystyle v=\sqrt {9.8 \times 15.5 \times \tan 11}=5.43 ms^{-1}$
for 13º v=5.92 and so on

can you see how the angle of incline changes with velocity to do the last part?
• Aug 18th 2008, 03:37 PM
topaz192
I am trying to understand what youre saying.
you used tan, does that mean i have to find cos and sin as well?
and where dis ms-1 come from?

and i noticed it increased, i just dont understand what that question is saying. lol
(Doh)
• Aug 19th 2008, 12:52 AM
thelostchild
nope you dont need to find sin and cos, theres no reason to using the formula your calculator does have a tan button on it!

the ms^-1 is just the unit of velocity meaning meters per second (its a good habit to get into giving every quantity such as length, area, time etc. that your working with units (Happy)

the runner in question wants to increase her angle of incline. When you increase the angle of incline the velocity increases, therefore to increase it further the runner must then increase their velocity

hope you understand this now
• Aug 19th 2008, 03:29 AM
topaz192