57 g tennis ball is traveling at 45 m/s to the right, when it hits a racket. the ball reverses direction and travels at 33 m/s. the ball is in contact with the racket for 0.0085 s. what is the magnitude of the force that was exerted on the ball? a-1.8 n b-12 n c-81 n d-520 n

As per the question the mass of the ball [m]=57 gram

1 gram,hence 57 gram =0.057 kg

The ball was initially moving with  velocity of 45 m/s to right.

Hence initial velocity[u] =45 m/s.

After reversing its direction due to the wall,the velocity of the ball was reduced to 33 m/s to the left.

Hence the final velocity of the ball [v] =33 m/s.

The time of contact of the ball with the wall [t] =0.0085 s

we are asked to calculate the force exerted by the wall on the ball.

First we have to calculate the impulse.

The impulse of a force is defined as  the change in momentum or the  force multiplied by time.

Mathematically impulse=force×time =change in momentum

                                              ⇒ F×t =m[v-u]

                                              ⇒

                                                           = [V= -33 m/s as it is opposite in direction]

                                                            = - 523.0588 N

The answer   is very close to   -520 N.

Hence option D is right. Here negative sign is due to the fact the force acts to the left i.e opposite to the direction of motion .

Force, F = 520 N

Explanation:

It is given that,

Mass of the tennis ball, m = 57 g = 0.057 kg

Initial speed of the ball, u = 45 m/s

Final speed of the ball, v = -33 m/s

Time of contact, t = 0.0085 s

Let F is the magnitude of the force that was exerted on the ball. It is equal to :

F = −523.05 N

Out of given options, the magnitude of force exerted on the ball is 520 N and it is acting in opposite direction.

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.