Question

While driving in the mountains, you notice that when the freeway goes steeply downhill, there are emergency exits every few miles. These emergency exits are straight dirt ramps which leave the freeway and are sloped uphill. They are designed to stop trucks and cars that lose their brakes on the downhill stretches of the freeway even if the road is covered in ice. You are curious, so you stop at the next emergency road. You estimate that the road rises at an angle of 15 degrees from the horizontal and is about 55 yards (165 ft) long.
What is the maximum speed of a truck that you are sure will be stopped by this road, even if the frictional force of the road surface is negligible?

Answer 1

Answer:

$v \approx 52.421\,\frac{ft}{s}$

Explanation:

The maximum velocity can be determined by the use of the Principle of Energy Conservation:

$\frac{1}{2}\cdot m_{truck}\cdot v^{2} = m_{truck}\cdot g \cdot s \cdot \sin \theta$

$v = \sqrt{2\cdot g \cdot s \cdot \sin \theta}$

$v = \sqrt{2\cdot (32.174\,\frac{ft}{s^{2}} )\cdot (165\,ft)\cdot \sin 15^{\textdegree}}$

$v \approx 52.421\,\frac{ft}{s}$