## Banked Curve

Track curves on race courses are steeply banked, which allow race car drivers to taken them at very fast speeds. If a particular course has a 125 m radius curve banked at 50°, what is the max allowable speed if the road is frictionless?

##
__
__**Hint**

**Hint**

$$$tan\theta =\frac{v^2}{rg}$$$

where
$$\theta$$
is the banked angle,
$$v$$
is the velocity,
$$g$$
is the acceleration due to gravity, and
$$r$$
is the radius.

##
__
__**Hint 2**

**Hint 2**

Use the equation to solve for velocity,
$$v$$
.

Start with:

$$$tan\theta =\frac{v^2}{rg}$$$

where
$$\theta$$
is the banked angle,
$$v$$
is the velocity,
$$g$$
is the acceleration due to gravity, and
$$r$$
is the radius. Thus,

$$$tan50^{\circ} =\frac{v^2}{(125m)(9.8m/s^2)}$$$

Solving for velocity,

$$$v=\sqrt{(125m)(9.8m/s^2)\times tan50^{\circ}}=\sqrt{(1.19)(1,225)m^2/s^2}$$$

$$$v=\sqrt{1,457.75m^2/s^2}=38.2\:m/s$$$

38.2 m/s