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3 years ago

13

An escalator is 18.3 m long. If a person stands on the escalator, it takes 47.8 s to ride from the bottom to the top. If a perso

n walks up the moving escalator with a speed of 0.521 m/s relative to the escalator, how long does it take the person to get to the top?

1 answer:

Novay_Z [31]3 years ago

8 0

Answer:

20.243 s

Explanation:

Because the escalator and person moving in the same direction, relative velocity can be calculated by summing the velocity of the escalator and velocity of the person.

The speed of escalator can be calculated as,

$v_{escalator}=\frac{x}{t}=\frac{18.3}{47.8}=0.383\ m/s$

Relative velocity

$v_{relative}=v_{escalator}+v_{person}\\\\v_{relative}=0.383+0.521=0.904\ m/s\\$

Therefore total time required to take the person to get to the top

$t=\frac{x}{v_{relative}}= \frac{18.3}{0.904}=20.243\ s$

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Explanation:

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$v_0$ is the initial vertical velocity of the ball.

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Horizontal displacement of the ball: $\Delta x = 0.352\;\text{m}$ ;
Time taken: $\Delta t = 0.440315\;\text{s}$

Assume that air resistance is negligible. Only gravity is acting on the ball when it falls from the tabletop. The horizontal velocity of the ball will not change while the ball is in the air. In other words, the ball will move away from the table at the same speed at which it rolls towards the edge.

$\begin{aligned}\text{Rolling Velocity}&=\text{Horizontal Velocity} \\&= \text{Average Horizontal Velocity}\\ &=\frac{\Delta x}{\Delta t}=\frac{0.352\;\text{m}}{0.440315\;\text{s}}=0.0799\;\text{m}\cdot\text{s}^{-1}\end{aligned}$ .

Both values from the question come with 3 significant figures. Keep more significant figures than that during the calculation and round the final result to the same number of significant figures.

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