Question

At some airports there are speed ramps to help passengers get from one place to another. A speed ramp is a moving conveyor belt on which you can either stand or walk. Suppose a speed ramp has a length of 120 m and is moving at a speed of 2.2 m/s relative to the ground. In addition, suppose you can cover this distance in 72 s when walking on the ground. If you walk at the same rate with respect to the speed ramp that you walk on the ground, how long does it take for you to travel the 120 m using the speed ramp?

Answer 1

It will take you 30.8 s to travel the 120 m of the ramp.

Step-by-step explanation:

Hi there!

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

x = x0 + v * t

Where:

x = position at time t

x0 = initial position

v = velocity

t = time

In this case, we will consider the start of the ramp as the origin of our reference system so that x0 = 0.

Now, let´s calculate the speed of the person walking on the ground:

x = v * t

120 m = v * 72 s

v = 120 m / 72 s

v = 1.7 m/s

If you walk on the ramp with that speed, your total speed will be your walking speed plus the speed of the ramp because both are in the same direction. Then, using the equation for the position:

x = v * t

In this case, v = speed of the ramp + walking speed

v = 2.2 m/s + 1.7 m/s = 3.9 m/s

120 m = 3.9 m/s * t

t = 120 m / 3.9 m/s = 30.8 s

It will take you 30.8 s to travel the 120 m