For a flourish at the end of her act, a juggler tosses a single ball high in the air. she catches the ball 3.3 s later at the same height from which it was thrown.
part a what was the initial upward speed of the ball?
express your answer to two significant figures and include appropriate units.

Initial speed of the ball, u = 16 m/s

Explanation:

It is given that, a juggler tosses a single ball high in the air. She catches the ball 3.3 s later at the same height from which it was thrown. Let u is the initial upward speed of the ball.

At the highest point, the final speed of the ball, v = 0

Using equation of motion as :

a = -g

Let are time of ascent and descent respectively.

So, total time,

u = 16.17 m/s

or

u = 16 m/s

So, the initial upward speed of the ball is 16 m/s. Hence, this is the required solution.

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.