Question

What is the smallest radius of a circle at which a cyclist can travel if its speed is 36 km/h, given that he bends by an angle 45° while turning [g = 10 $m/s^{2}$]

Answer 1

Hi friend

first convert the velocity from km/h to m/s

v= 10 m/s

Using the formula

tan θ = v2/rg

tan 45 = 10×10/r×10

1=10/r

r= 10 m

hope you understood

Answer 2

The smallest radius of the circle made by cyclists is 10m.

Given,

Speed of cyclist = 36km/h

The angle of the cyclist =45°

$g \: = 10 \frac{m}{ {s}^{2} }$

To Find,

The smallest radius of the circle is made by the cyclist.

Solution,

We can solve this type of problem in the following manner.

The factors of Normal response for cyclists want to fulfil the equation of dynamics i.e. helping the weight & centripetal force.

So,

$n \sin(q) \: = \frac{m {v}^{2} }{r}$

equation first.

$n \cos(q \: ) = mg$

equation second.

on dividing the first equation by the second equation

$\tan(q) = \frac{ {v}^{2} }{rg}$

$r = \frac{ {v}^{2} }{g \tan(q) }$

$r = \frac{10 \times10 }{10 \times \tan( {45}^{.} ) }$

r = 10m

Therefore, the smallest radius of the circle made by cyclists is 10m.