A6.25-kg bowling ball moving at 9.4 m/s collides with a 0.875-kg bowling pin, which is scattered at an angle of \theta =83.5 degrees from the initial direction of the bowling ball, with a speed of 17.5 m/s.(part a) calculate the direction, in degrees, of the final velocity of the bowling ball. this angle should be measured in the same way that \theta is.(part b) calculate the magnitude of the final velocity, in meters per second, of the bowling ball.

A)

B) v = 9.47 m/s

Explanation:

Given:

mass of the bowling ball, m₁ = 6.25 kg

Initial velocity of the ball, v₁ = 9.4 m/s

mass of bowling pin, m₂ = 0.875 kg

velocity of the pin, v₂ = 17.5 m/s

Angle of scatter, Θ = 83.5°

a)The direction of the final velocity of the ball (∅)

on substituting the values in the above equation, we get

or

or

or

B) From the concept of conservation of momentum

we have

on substituting the values

we get

hence, the magnitude of the final velocity

v = 9.47 m/s

change tension

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.