Question

A skateboarder rolls horizontally off the top of a staircase at a speed of

14.5 ms and lands at bottom of the stairs. The staircase has a horizontal length of
8.00m 8.00m8, point, 00, start text, m, end text. We can ignore air resistance. What is the skater's vertical displacement during the jump?

Answer 1

The answer is -1.49 m not 1.49 m

Step-by-step explanation:

It is referencing displacement from a higher point to a lower.

Answer 2

The skater's vertical displacement during the jump is 1.49 meters

Step-by-step explanation:

Horizontal Motion

When an object is thrown horizontally with a speed v from a height y, the range or maximum horizontal distance traveled by the object can be calculated as follows:

`\displaystyle x=v\cdot\sqrt{\frac {2y}{g}}`

If we already know the value of x, we can solve the above equation for h:

`\displaystyle y=\frac {x^2g}{2v^2}`

We use the given values v=14.5 m/s, x=8 m,
`g=9.8 m/s^2`:

`\displaystyle y=\frac {8^2\cdot 9.8}{2\cdot14.5^2}`

y = 1.49 m

The skater's vertical displacement during the jump is 1.49 meters