Asolid wood door, 90.0 cm wide by 2.00 m tall has a mass of 35.0 kg. it is open and at rest. a small 500-g ball is thrown perpendicular to the door with a speed of 20.0 m/s and hits the door 60.0 cm from the hinged side. the ball rebounds with a speed of 16.0 m/s along the same line. what is the angular speed of the door just after the collision with the ball ?

w = 1.14 rad/s

Explanation:

Moment of inertia ()

Moment of inertia = 35 * 0.9^2 / 3 = 9.45 kg m^2

Impulse ("An impulse is equal to the net force on the object times the time period over which this force is applied. ")

Impulse = 0.5 * [16 - (- 20)]

Impulse = 18 kg m/s

angular momentum = M of I *angular speed  w

= 9.45 w

= impulse * distance  

= 18 * 0.6

 9.45 w = 18 * 0.6

w = 1.14 rad/s  

where is the photo and the answer choices?

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.