A skateboarder rolls horizontally off the top of a
staircase at a speed of 18 ms-1
and at the bottom of
the stairs which has a horizontal length of 9 m as
shown.
Calculate the skater's vertical displacement during
the jump?

Given Information:

Initial horizontal speed = Vx = 18 m/s

horizontal distance = R = 9 m

Required Information:

Vertical displacement = h = ?

Vertical displacement = h = 1.23 m

Explanation:

The horizontal distance covered by the skater is given by

R = Vx*t

Where R is horizontal distance, Vx is the initial horizontal speed and t is the time taken for the jump.

t = R/Vx

t = 9/18

t = 0.5 seconds

The vertical displacement covered by the skater is given by

h = Vy*t + ½gt²

Where Vy is the initial vertical speed of the skater and is zero since the skater jumps horizontally, g is the gravitational acceleration and h is the vertical displacement.

h = 0*t + ½gt²

h = ½gt²

h = ½(9.81)(0.5)²

h = 1.23 m

Therefore, the vertical displacement of the skater is 1.23 m

the moving of the box is a result of centripetal force. think of that  as a car or a truck in this case creates a turn, the force of friction performing upon the turned wheels of the car runs centripetal force obligatory for circular motion for the things inside it.