On a trip through Parley\'s Canyon on Interstate 80, you notice that when the ro
ID: 1524342 • Letter: O
Question
On a trip through Parley's Canyon on Interstate 80, you notice that when the roadway goes steeply down a hill, there are emergency exits every few miles. These emergency exits are straight ramps which leave the main roadway and are sloped uphill. They are designed to stop runaway trucks and cars that lose their brakes on downhill stretches of the freeway even if the road is covered with ice. You are curious, so you stop at the next emergency exit to take some measurements. You determine that the exit rises at an angle of 10 degree from the horizontal and is 100 m 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?Explanation / Answer
net force along the incline is -mg*sin(theta) = ma
m cancels on both sides
accelaration a = -g*sin(10) = -9.81*sin(10) = -1.703 m/s^2
distance travelled before stopping is S = 100 m
final speed is v = 0 m/sec
initial speed is Vo = ?
using
V^2-Vo^2 = 2*a*S
0^2 - Vo^2 =-2*1.703*100
Vo = 18.5 m/sec