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 118 m and is moving at a speed of 1.9 m/s relative to the ground. In addition, suppose you can cover this distance in 76 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 118 m using the speed ramp?

Answer 1

To travel 118 m using the speed ramp, it would take approximately 62.11 seconds.

Step-by-step explanation:

To determine how long it takes to travel the 118 m using the speed ramp, we need to calculate the relative velocity of the person walking on the ground concerning the speed ramp. Since the person walks at the same rate on the ground as they do on the speed ramp, the relative velocity between them is zero. Therefore, the person's walking speed is equal to the speed of the ramp, which is 1.9 m/s.

Using the formula distance = speed x time, we can rearrange it to solve for time: time = distance/speed.

Therefore, the time it takes to travel the 118 m using the speed ramp is 118 m / 1.9 m/s = 62.11 seconds.

Answer 2

It takes 34.173 s

Step-by-step explanation:

This is a relative movement exercise.

We are going to use that :

`Speed = (distance)/(time)`

And the relative movement velocity equation :

Given a particle P, and two reference systems A and B in which we know the velocity from system B relative to A and the velocity of P relative to B :

`V_(P/A) =V_(P/B) +V_(B/A)`

Don't forget that this is a vectorial equation.In our exercise the person velocity and the speed ramp velocity have the same direction so we turn the vectorial equation into a scalar equation.

We can cover 118 m in 76 s ⇒
`Speed=(distance)/(time) \\Speed=(118m)/(76s) \\Speed=1.553(m)/(s)`

This will be our speed relative to the speed ramp

`S_(person/ramp) =1.553(m)/(s)`

`Speed_(ramp/ground) =1.9(m)/(s)`

We use the equation (in terms of speed) :

`Speed_(person/ground) =Speed_(person/ramp) +Speed_(ramp/ground)=\\ Speed_(person/ground)=1.553(m)/(s) +1.9(m)/(s) \\ Speed_(person/ground)=3.453(m)/(s)`

Then →

`Speed_(person/ground) =(distance)/(time) \\3.453(m)/(s) =(118m)/(time) \\time=(118m)/(3.453(m)/(s) ) \\time=34.173s`