Question

A speed ramp at an airport is basically a large conveyor belt on which you can stand and be moved along. The belt of one ramp moves at a constant speed such that a person who stands still on it leaves the ramp 64 s after getting on. Clifford is in a real hurry, however, and skips the speed ramp. Starting from rest with an acceleration of 0.37 m/s2 , he covers the same distance as the ramp does, but in one-fourth the time. What is the speed at which the belt of the ramp is moving?

Answer 1

The speed at which the belt of the ramp is moving is 11.84 m/s.

Step-by-step explanation:

To find the speed at which the belt of the ramp is moving, we can use the concept of relative velocity. Let's assume that the speed of the belt is vramp. Since Clifford covers the same distance as the ramp does, but in one-fourth the time, his time is 64/4 = 16 seconds. His initial velocity is 0 m/s and his final velocity can be calculated using the equation v = u + at, where u is the initial velocity, a is the acceleration, and t is the time. Substituting the given values, we have v = 0 + 0.37 * 16 = 5.92 m/s

Now, we can find the speed of the belt using the equation vramp = v - vp, where vp is the velocity of Clifford relative to the ground. Since Clifford and the belt leave the ramp at the same time, their velocities should cancel each other out. So, vp = -5.92 m/s.

Substituting the values, we have vramp = 5.92 - (-5.92) = 11.84 m/s.

Answer 2

The belt ramp is moving at 0.047 m/s

Step-by-step explanation:

Hi!

The equation for the position of an object moving in a straight line with a constant acceleration is:

x = x0 + v0 * t + 1/2 * a * t²

where:

x = position at time "t"

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

If the object moves with constant speed, then, a = 0 and x = x0 + v * t

First, let´s find the lenght of the speed ramp by calculating the distance walked by Clifford.

x = x0 + v0 * t +1/2 * a * t²

x0 = 0 placing the origin of our reference system at the begining of the ramp

v0 = 0 Clifford starts from rest

t = 64 s / 4

a = 0.37 m/s²

Then:

x = 1/2 * 0.37 m/s² * 16 s = 3.0 m

Now that we know the lenght of the speed ramp, we can calculate the speed of the ramp which is constant:

x = x0 + v * t x0 = 0

x = v * t

x/t = v

3.0 m / 64 s = 0.047 m/s