For a simple 15 upward ramp, what length would be needed for a runaway truck traveling 140 ?
To determine the length of the ramp needed for a runaway truck, we need to consider the speed of the truck and the inclination of the ramp.
In this case, let's assume that the truck is moving at a constant speed of 140 miles per hour (mph) or approximately 63 meters per second (m/s) when it reaches the bottom of the ramp.
To calculate the length of the ramp, we need to use the formula for the distance traveled by an object on an inclined plane:
Distance = (Speed^2) / (2 * Acceleration * Inclination)
Given that the acceleration due to gravity is approximately 9.8 m/s^2 and the inclination of the ramp is 15 degrees, we can calculate the length of the ramp.
Step 1: Convert the inclination from degrees to radians:
Inclination (in radians) = Inclination (in degrees) * π / 180
In this case, the inclination in radians would be:
Inclination (in radians) = 15 * π / 180 = 0.2618 radians (approximately)
Step 2: Calculate the length of the ramp:
Distance = (Speed^2) / (2 * Acceleration * Inclination)
Distance = (63^2) / (2 * 9.8 * 0.2618)
Distance ≈ 895.4 meters
Therefore, to bring the runaway truck to a stop safely, a ramp of approximately 895.4 meters in length would be needed for a 15-degree upward slope.