A highway curve of radius 80 m is banked at $45 ^ { \circ }$ Suppose that an ice storm hits, and the curve is effectively frictionless. What is the speed with which to take the curve without tending to slide either up or down the surface of the road?
A) 28 m/s
B) 780 m/s
C) 9.4 m/s
D) The curve cannot be taken safely at any speed.

Question

A highway curve of radius  80 m is banked at $45 ^ { \circ }$ Suppose that an ice storm hits, and the curve is effectively frictionless. What is the speed with which to take the curve without tending to slide either up or down the surface of the road?
A)  28 m/s
B)  780 m/s
C)  9.4 m/s
D) The curve cannot be taken safely at any speed.

Quizplus · Accepted Answer

The speed to take a frictionless banked curve without sliding is given by $v = \sqrt{rg\tan(\theta)}$, where $r$ is the radius of the curve, $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$), and $\theta$ is the banking angle. Plugging in the given values ($r = 80 \, \text{m}$, $\theta = 45^\circ$), we get $v = \sqrt{80 \times 9.8 \times \tan(45^\circ)} = \sqrt{80 \times 9.8} = \sqrt{784} = 28 \, \text{m/s}$.

A Highway Curve of Radius 80 M Is Banked 45∘45 ^ { \circ }45∘

A Highway Curve of Radius 80 M Is Banked $45 ^ { \circ }$